There are a wide range of fun sports and outdoor activities in Italy, among them the following:
hiking, camping, and backpacking.
SCUBA diving. Napoli Soccer Game. Avellino
Unfortunately, for the golf addicts out there, the sport has not caught on in Italy the way that it has in other European countries and much of Italy's lush verdant undulating landscape is completely underutilized. There is more golf in Northern than Southern Italy but still nothing that compares with large number of golf courses you would find around most US cities.
There are two golf courses in the Naples Area:
There are a number of golf courses near Rome but they can be expensive. Le Querce and Castel Gandolfo are both recommended. For more information, google.
Roccaraso is among the closest ski resort areas, with a busses leaving from Carney Park during the season. They also have snow tubing. Campitello Matese and Campobasso are closer, smaller resorts.
Nisida hosts the Naples NATO Yacht/Sailing Club, which any military person can join for about €80 a year; membership gives you the docking privileges and free rental of their smaller sailboats. Kayaks can be rented from Carney Park, and various seaside vendors allow you to rent kayaks, rowboats, or motor boats.
Rent a gomma (inflatable RHIB-like boat) out of Monte di Procida ~€150 (6 pax): Locaboat Cell 333-336-8189 [3339272410/3384207770/0818045366]
Naples hosts a marathon and half-marathon in April; see the events page for more. Some good places to run include the various lungomare (along the water, e.g. Pozzuoli, Mergellina...) and the huge park of Capodimonte. If you like rough trail running and hills, Carney Park has nice paths (see the hiking page for more information). There is also a hashing kennel, the Bella Napoli Hash House Harriers, although they are a self-described "drinking club with a running problem"
In addition to the Support Site and JFC bowling alleys, there are the following bowling alleys out in town:
The Climbing House club on the Amalfi Coast has information about several good sites on/near the coast. You can do "via Ferrata" climbing in the Dolomites or Gran Sasso Park (see the Hiking Page for more information). [OTHER CLIMBING SPOTS??] For climbing gear, check out Decathlon and ask for "arrampicata" gear.Marmore Falls in Umbria and on the Lao River in Calabria's Pollino National Park (which extends into Basilicata). See other adventure sports.
Maybe not a "sport" but fun nevertheless--check out the Basilicata page for information about the "Volo dell'Angelo" between two hilltowns in southern Italy.