Exeter! (Or Stratham, Kensington, East Kingston, South Hampton). Exeter school district is good and the town is super cute. 20 minutes to Portsmouth and theres a train stop right in town to get down to Boston in just over an hour. Not a ton on the market, though. I'm from Kingston which is right nearby and while there are some nice homes and it is nicer than some abutting towns, it might only be something to consider if you want to maximize square footage and acreage. It's kind of rural in the sense that there isn't much of a downtown and the school is very okay.

Durham is nice but UNH kind of rules the town. Newmarket is coming up but very small school. Rye is gorgeous if you can afford it. Greenland is also a great option, right outside of Portsmouth.