The following blogs are written by English speakers (mostly expats) who live (or lived) in Naples and the rest of Campania:
Karen Phillips' AndiamoTrips - an American who has lived in Naples >20 years, Karen leads a bunch of food & wine events (I went on some, they're amazing!)
Jeff Matthews' Naples Life Death & Miracles - originally from LA, Jeff has lived in Naples for over 40 years (!), and his blog gives a bunch of interesting information at Neapolitan culture and history
...there are also a bunch of English-language bloggers on the Amalfi Coast:
Laura Thayer's Ciao Amalfi - American Laura wrote the Moon guidebook to the Amalfi Coast, so she knows her stuff!
Rompipalle's Under the Neapolitan Son - woman from Brooklyn writing about motherhood and life in Naples, not updated since 2015
Alex's 2 Ciaos - Greek-American who lived in and blogged about Naples until moving to Califiornia in late 2007, not updated since 2012
Livin' Italian - American living in Naples, not updated since 2016
No longer online:
Amanda Mulock Murray's Living in the Boot
Robert Bishop's The Bishop Blog
Karen C's The Shock of the Old - KC has a PhD in art history, also raising toddlers in Sessa Aurunca
Karen Margaret Landes' South of Rome (author of a book about Sicily who lived in Santa Maria Capua Vetere from August 2007 to March 2009 and thus has various posts about Naples)
Marylee in Pozzuoli - letters and photos by a Navy wife