We are an hour from Lake George and go there often. There are tons of family friendly activities in that area. We're headed over to the drive in movies this weekend. The lake is pretty with a tourist village with shops, restaurants and touristy stuff like haunted houses and wax museums. There are a couple of amusement parks (one is Six Flags), water parks, lots of mini golf, go carts and arcades, outlet shopping, a French and Indian War era fort, boat rides on the lake (we'll be on a dinner cruise on the lake next month). Lots of hotels including the Great Escape Lodge with and indoor water park. The Comfort Inn and suites has a nice little indoor pool area with water slide and a kiddie pool with fountain. They also have a nice playground and grills and picnic tabels out back. Country Inn and Suites is right next to the Six Flags park so you can walk. We've stayed at all 3 of the above and had a nice time.
Our favorite weekend getaway is the Portsmouth, NH area. In Portsmouth there is Strawberry Banke museum, a water park and Odiorne State Park. We also go up to Kittery for the outlets and York. It is really nice to stay right in Portsmouth (love the Sheraton Portsmouth Harborside, but it is pricey), but it is really not necessary. For budget accomodation there are some nice hotels in the Dover area that can be had on Hotwire for a really reasonable price. Dover is about a 15-20 minute drive to everything and has the children's museum.