Throughout England, the Michelin guide is good for finding good places to eat (we had the best luck filtering by price—that tended to show "fancy pubs"). In some areas there are local guides (e.g. Western England has "Taste of the West").
London is always a great idea! With so many museums, historical sites, royal homes & gardens, and world-class shopping & dining, there's always plenty to do in this world capital. London is easily accessible from Naples Capodichino airport via non-stop flights into Gatwick and Stanstead airports on British Airways and EasyJet. Both airports are within easy commuter distance on non-stop train service to Victoria station (from Gatwick, 30 minutes) & Liverpool Street station (from Stanstead, approx. 30 minutes). Both stations are centrally located & connected to the overall London Tube system. However, be advised that on some major UK holidays (i.e. Boxing Day), Tube workers will sometimes strike, forcing you to actually get to those stations via taxi before getting on the airport express trains.
London at Christmas is an especially good idea, truly the stuff of Dicken's "A Christmas Carol." For a truly festive time on Christmas Eve, check out the Christmas Eve Carol Service at St. Paul's Cathedral (4pm) or various masses at Westminster Abbey, including a midnight mass. Reservations/tickets are not required, however, be sure to arrive early (as early as 3pm to St. Paul's and 9:30pm for midnight mass at the Abbey), in order to queue up. Lines can be very long and late arrivals are turned away once the churches are filled to capacity. If attending midnight mass at the Abbey, it is advisable to reserve a taxi ahead of time, lest you stand on a cold street corner trying to flag one down at 1:30am on Christmas Eve. Reserved taxis will wait just outside the Great West Door entrance. For Christmas Day dining options, be prepared to pay a premium at high-end restaurants (upwards of 100 pounds/person), but many smaller pubs offer Christmas Day dining for around 30 pounds/person as well. Most large businesses, shops, etc. (such as Harrods) are closed on Boxing Day (Dec. 26), but some stores and major shopping areas/centers (i.e. Regent Street, Savile Row, Oxford Circus, Sloane Square, etc.) are beginning to stay open on Boxing Day to offer post-Christmas sales.
Places to eat
Dishoom - really nice Indian food, a few different locations
Fallow - upscale British food, rec'd Michelin
Bath
A fantastic example of Georgian architecture, Bath is an excellent center for commerce, shopping & historical sight-seeing. Be sure to check out the Bath Abbey which contains one of the world's finest examples of fluted-vaulting within the nave. Adjacent to the Abbey are the ruins of the Roman public baths (yes, where the city derives its name), which is an impeccably curated museum & a must-see for visitors already familiar with Roman historic sites within Italy (contains an excellent giftshop, as well!). The shopping district of Bath surrounds the plaza containing the Abbey & Roman baths and is quite comprehensive with many British name brand shops & chain restaurants (i.e. Monsoon, Gieves & Hawkes, Conwall Pasty Co, etc.), but also lots of local pubs and specialty stores. For Jane Austen fans, Bath houses the Jane Austen Museum in a home where she once vacationed just blocks from the Bath Circus area (nicely presented with an excellent bookshop).
Stonehenge
Situated in the Salisbury Plain of England (along with many other mystical, religious & neolithic sites), Stonehenge is approximately a 2-hour drive from London. While it's certainly the most famous of the sites in this part of the UK, it's not the only one in the area that bears mentioning.
Glastonbury
Home of the famous annual music festival, approx. 1 hour from Stonehenge, boasts beautiful abbey ruins (from Henry VIII's dissolution of the abbeys) and sites pertaining to the legend of King Arthur. The Glastonbury Tor has been revered as the reputed site of "Avalon" for centuries and the summit can be reached via a lovely hike through pastoral fields to reach the bell tower ruin of St. Michael's. At the foot of the Tor lies the Chalice Well, which is purported to contain healing waters & is said to be where Joseph of Arimathea buried the chalice used by Christ at the Last Supper. The Arthurian legend attracts a number of "new age" people so there are some interesting hippie shops, too. Nearby Wells Cathedral is also worth a visit.
***Abbey Tea Rooms & Restaurant - Luke's favorite "cream tea" (scones with clotted cream & jam), as well as an excellent "plowman's" (hearty but simple lunch of bread, cheese, and cured meat)
Bocabar - a casual but pretty good-quality spot
Hundred Monkeys Cafe - a bit hippy, nice and cozy
Other West England Sites near Stonehenge
Also within easy driving distance of Stonehenge for more Arthurian-enthusiasts, is the beautiful town of Winchester. The Great Hall of Winchester Castle is the finest surviving example of medieval great halls & the only original portion of the castle that remains. It dates from the reign of William the Conqueror (1066-1087) and houses a replica of the famous Round Table, constructed and painted in the 13th century. Excellent high street shopping & a beautiful cathedral (burial place of Jane Austen) in Winchester, as well.
For those interested in British Naval history, do not miss Portsmouth, home to one of the most famous ships in history, the HMS Victory! A truly excellent experience with museum collections, memorabilia, one of the sails from the famous Battle of Trafalgar and plenty of Admiral Lord Nelson images (for the ladies, naturally!). Admission also includes a guided tour of the Victory by active-duty sailors in the Royal Navy.
Avebury
If you like Stonehenge but want to get closer to some ancient stones, Avebury's your place! The town is surrounded by many, many standing stones
***The Bell - in West Overton outside of Avebury, delicious food in a "fancy pub"
Dartmoor
The setting of the Sherlock Holmes "Hound of the Baskervilles" novel, this is a beautiful and wild place...but also some old farms and towns
***Haytor Rocks - perhaps the most photogenic site in Dartmoor
Places to Eat
***Riverford Field Kitchen - just South of Dartmoor Park, "farm to table" cooking, delicious and fresh!
The Dartmoor Inn - on the west end of the park near Lydford/Okehampton, nice food
The Gateway Tea Room & Cafe - nice tea room in Moretonhampstead, cute china, kid friendly (they have books & games & high chairs)
The Chagford Inn - in Chagford (duh), very nice food
Places to Stay/Eat
Gooseford Farm - B&B on the north end of Dartmoor, has a bunch of animals, hearty meals served
Cornwall
Boscastle Farm Shop - nice, very popular spot for breakfast/lunch near Tintagel
***The Kingham Plough - delicious food and comfortable rooms
***Daylesford Kingham - a beautiful farm/shop/restaurant
Good source for information: Scotland the Best book
Scotland's capital, and home to a bunch of interesting history (including the Scottish Crown Jewels)
Scotland's more gritty—but very interesting—city, to the West of Edinburgh
"The Highlands" refers to north/western Scotland, where at least traditionally Gaelic was more common, which tends to be less-populated but very beautiful.
Isle of Skye
One of the largest islands, and one of the easiest to get to from the mainland (there's a bridge, but you can also take a ferry). This beautiful, rugged place featured in several movies.
Things to See
The Quiraing - other-worldly cliffs and mountains
Old Man of Storr - rocky outcropping
Fairy Pools - beautiful pools/waterfalls in a valley, but be prepared for midges! (some people wore beekeeper-like hoods; at a minimum have bug spray and long sleeves...we also went to the Fairy Glenn which was not quite as interesting) ...limited parking
Neist Point/Lighthouse - beautiful outcropping leading to a lighthouse, with sheep all around, at the westernmost point; the roads leading there get a bit curvy/narrow
Dunvegan Castle - cool castle with nice gardens, has an interesting history
other stuff
Skye Weavers - cool spot for handmade wool
Skyeskyns - tannery (we didn't make it there but it looked interesting)
Places to Eat
Isle of Skye Baking Company - in Pointree, nice bakery with art gallery
also in Pointree, we didn't try but looked good: The Granary Cafe, Scorrybreac Restaurant, The Caledonian Cafe
Ellishadder Gallery - nice place to eat near Storr/Quiraing
Old Byre Skye - nice little spot for breakfast, also has art
Old School Restaurant - as the name suggests, a bit old school, but a nice spot to eat near Dunvegan Castle
The Three Chimneys - very fancy, very nice place to eat
Kinloch Lodge - recommended place on the south end of the island (but we didn't eat there)
Single Track Art Gallery & Espresso Bar - north end of island, not far from Quiraing, we didn't go but looked good
Loch Bay Restaurant - looked good but we didn't go
Cafe Lephin - nice little spot, not far from Neist Point
Red Roof Skye - nice little cafe on the way to Neist Point
Good source for the best food/hotels: John and Sally McKennas' Guides (formerly Bridgestone Guides)
2 things are especially popular with American tourists: learning about the Troubles (sectarian conflicts between the Unionists and Republicans) and touring Game of Thrones locations (among the most popular is this one, which is mostly led by people who were extras)
Capital of the Republic of Ireland, home to many multinational companies' European operations, and the biggest city on the island.
Things to Do
Powerscourt Centre - nice place to shop
Guiness Factory - a bit of a tourist trap but you do learn a lot about how Guiness is made, and how to pour it...and the bar on the top is gorgeous on a clear day
Places to Eat
?Hatch and Sons - looks like a nice breakfast/lunch place
Dunne and Crescenzi - not bad Italian restaurant
Bunsen - quick place for good burgers, in Temple Bar area
Wilde Restaurant - somewhat upscale, good food
Newgrange - can be done as a day trip, is older than Stonehenge!
Eastern Seaboard - nice place to eat in Drogheda, not far from Newgrange
Malahide - town north of Dublin, has a castle/gardens, it's close to the airport so it's a good place to stay on your way out if you have a car
Jaipur - great Indian restaurant, rec'd Michelin
Lovely town on the west coast of Ireland with a walkable center, great food, and a lot of young people (thanks to its university).
***Kai Restaurant - west of the River Corrib, amazing, innovative dishes; also reasonably kid-friendly (they gave our 1.5 year old the best fish sticks he'd ever had!)
***Ard Bia Restaurant - near the port, this tiny, casual place has amazing Irish traditional dishes with fresh ingredients
The Cliffs of Moher - a little ways south of Galway, beautiful cliffs with a view of the Atlantic (but watch the weather—sometimes the visibility is bad)
Stonecutters Kitchen - nice place for a meal not far from Moher
Aran Islands - a beautiful, interesting place where many of the locals still speak Irish as their first language; ferries leave from Doolin or outside Galway
Bayview Restaurant - our favorite place to eat, near the port
Teach Nan Phaidi - another nice place to eat, near the entrance to Dún Aonghasa
Aran Islands Goats Cheese - nice spot, we went on a van tour with the owner!
### add more here
Kildare
Harte's - nice pub with great food (especially french fries!), rec'd Michelin