We're in the opposite situation, we're in NH and want to go where it's warm! We usually don't make it too far in the summer months because my DH gets tied up with work, so Boston (Fenway) and midcoast ME are as far as we usually make it, though this year we'll try attempt to get to Florida and Las Vegas (or Dallas) in early June if at all possible (I think they'll both be too hot though, neither sound too promising at the moment).
By the way, we live in a pretty big "Summer destination region" ourselves, seacoast NH. If anyone's interested, here's some detailed infromation from the point of view of a life-long local. It is a beautiful area, but you have to hit the right places. Portsmouth, the "main attraction" is a great seaside city to visit for the day, Newberryport MA (about 30 minutes away) is very similar and quite clean, both have nice dining.
The best beaches are in ME, avoid Hampton Beach (DIRTY beach town) and Seabrook NH (Nuclear Power Plant) at all costs, the Kennebunk area, which is only about 25 minutes away from Portsmouth, has some gorgeous beaches if you're looking to go somewhere secluded. For a nostalgic little beach town I'd reccomend going to York Beach ME (much cleaner than Hampton NH), it's very close to Portsmouth. The best beach in NH is in Newcastle, just south of Portsmouth. The area off the beach houses the Seacoast Science Museum, it's somewhat new and they have lots for kids to do. The beach itself is also the best place for tide pools, there's lots of horseshoe carbs and sandollars to be found. You can also take ferries from Portsmouth, to the Isles of Shoals, a small group of islands off the coast.
As far as where to stay goes, I'd suggest the Hilton Garden Inn in Portsmouth, which is brand new in the city center, or the Marriott Wentworth by the Sea, in Newcastle, which is a harbor-front big renovated victorian hotel (like the Breakers on a smaller scale). There's lots of small places in Southern ME, the White Barn in is the most luxurious.
I'd avoid all of the theme parks, Canobie Lake isn't safe (and I'll admit it, has a pervert problem

) and York's Wild Kingdom is the most disgusting and unkeeped zoo I've ever been to. If you're looking for thrills, go to Six Flags in MA. There are quite a few historical museums that are great if you're interested. The shopping is okay, MUCH better in Boston, but there are two malls on the smaller side, one more near ME and one more near MA, and Tanger outlets in Kittery ME, right near Portsmouth.
I hope I haven't scared any of you away, it really is a nice area worth visiting. There's a lot of history here, many houses (some you can tour) are from the 1600's. It's a great place to fish, overall there's lots of sea life. If you're in the Boston area, I would definately urge you to come for a few days or even just an afternoon.