We always enjoyed city trips at that age--Pittsburgh, Philadelphia, Baltimore, Indianapolis, Miami, St. Louis. Honestly, anywhere that has a zoo, aquarium, a children's museum, nice playgrounds, small amusement parks. Add in a hotel pool and the kids will have fun.
If you want to go to the beach, just do a weekend at one of the MD/DE/NJ beaches but go the first week of school. It will be empty but still warm enough to swim and the hotels will be cheap.