Dante's in Barrington is a pretty good italian restaurant. But Ristorante Massimo in Portsmouth is the tops around here (pricey and exclusive... reservations required). Another really good restaurant is The Farm in Dover. I am also partial to Barrio in Portsmouth (tacos).

The Press Room in portsmouth frequently has live music. I haven't been there in ages... but I'm going this saturday to see a show. Stone Church as someone else mentioned in Newmarket has live music frequently as well.
If you're just driving around looking at the area and want to kill some time during the day... Crackskull's Coffee and Books in Newmarket is an awesome little coffee shop. Might want to consider Newmarket as a potential place to live as well. There's also a trail along the Lamprey River in Newmarket... access through a trailer park on the opposite side of the river from downtown.

For walks.. can't go wrong at Odiorne state park.. then drive the coastline, stopping at different places to gaze at the ocean.