I can't think of any lighthouses off the top of my head, besides the one in Watch Hill, Rhode Island.
In Connecticut you can stop in Mystic. It's really beautiful there. You'll find some great resteraunts and you could shop in some boutique type shops in Olde Mystic Village. The Saybrook Fish House or the Steak Loft are great places to get a good meal. I've stayed at the Comfort Inn in Mystic and it was really nice and affordable.
In Maine I would go to Brunswick. Another really beautiful town with a great downtown area as well as beautiful waterfronts. Kennebunkport is nice too. Don't forget Freeport for shopping

Basically anything in the Casco Bay or the Sebago Lake areas are very nice.
New Hampshire has the White Mountains and Hurst Turkey Farm.
Forest Park in Springfield is a great place to stop if you have children with you. They have a cool petting zoo. Bring a lunch and go to the park.