For Boston, here are some music recs. A lot has changed as far as food, shops, etc. so I'll leave that up to other folks to weigh in.
For NH and into Maine, it depends on how far north you're going. The NH and Southern Maine seacoasts are amazing, but Acadia National Park is kind of the crown jewel of coastal hiking/sightseeing. Mt. Major in NH is one of the best effort-to-payoff hikes around. Portsmouth, NH is great for walking around and popping into random shops and restaurants. Portland, ME has some of the best food in the country, but there are too many places to even list (Duckfat is a long-standing classic.)
If you have more specific spots or interests, I can add more details!
