Cities are good weekend destinations because the people that live there typically leave for the shore or the country.
Philadelphia gets overlooked. It's cheaper than its neighbors New York City and Washington, D.C., and there are lots of fun things to do -- world class museums, historic sites, great dining, all at more affordable prices. There are also a lot of great sites in the area -- Lancaster County, Longwood Gardens and Valley Forge.
Texas Hill Country, Austin is great, too. It's affordable and really gaining in popularity. The New York Times named it one of the top places to go this summer. Austin and San Antonio are two great cities to see because they are really unique, offering great music, Tex-Mex and barbecue, as well as outdoor activities like dude ranches, national parks and hiking.
Summer is off-season at ski resorts, so you can get great deals, and you can enjoy plenty of outdoor, family-focused activities at reduced rates. Kids love riding the gondolas, hiking, mountain biking, horseback riding, and a lot of places have alpine slides (similar to sledding on luge-like tracks) (Check out Stow, Vermont and Breckenridge, Colorado.)