New England is my neck of the woods, and we certainly have our fair share of fun things. For MA, I would recommend --
Sturbridge Village, Plimouth Plantation (Plymouth), Battleship Cove (Fall River), Edaville Railroad (Carver) -- These would appeal most to parents and kids with a real interest in history of various sorts.
Drumlin Farm (Lincoln), Joppa Flats (Ipswich) - These are Audobon preservation areas. The first one is a working farm. Both have lots of outdoor fun activities for kids. These are NOT boring.
Endicott Park/Farm (Danvers MA) - Tons of fun for about $5 a group. This is a working farm with animal petting/feeding opportunities, a huge outdoor play structure, hiking in the woods with self-guided exercise stations, picnic area.
Hammond Castle (Gloucester) - A real castle of sorts created by an eccentric who imported parts of real buildings from Europe. An enormous pipe organ is built into the walls, and it even has its own weather. Tons of cool activities here like Renaissance Faires.
Discovery Museum (Acton) - Two small museums (Science + Kids) on same lot. This is not a huge, state of the art museum by any means, but it is so much more relaxing, fun and cheap when compared to the Boston Children's museum. Age range would likely be 12 and under.
Salem is not just witches. There is certainly a Halloween aspect to it. However, there is pirate museum, a tall ship in harbor, art galleries, street vendors/performers, and the Willows; a strip along the ocean with arcades, greasy spoon restaurants, ferry rides and kiddie rides. There's also highly entertaining Ghost/Witch/History/Architecture-themed tours running continually. It's hard to go wrong with Salem.
As for New Hampshire... There's the weirdly fascinating "American's Stonehenge." There are tons of kitsch amusement parks like Storyland, Santa's Village, and Clark's Trading Post. Canobie Lake Park is a huge (for this area) amusement park. The Flume is a breath-takingly beautiful gorge that one hikes through.
Oh, and Maine... York Zoo is a zoo and amusement park that is very close to the MA border. It's quaint, but it is also fun, cheap and easy to manage when compared to huge, busy attractions like Roger Williams or Canobie Lake.
Hope this helps. ~ N