I went on a spring break trip to Galveston, TX in 2009. Galveston is a popular spring break destination for college kids and twenty-somethings, especially southern kids who don't want to travel all the way to Cancun or Florida. After making a few trips to Panama City, another popular spring break spot, I can confidently say that Galveston is actually quite clean for a spring break destination and is a little more relaxed during the spring break season than other places. We stayed at the Quality Inn and Suites but there are nicer hotels for the non-spring break crowd, such as the The Tremont House, which is a Wyndham hotel. The downtown area of Galveston is very nice, and historic looking and has lots of surprisingly cute shops and restaurants.
If you're looking for the best place to eat in the area, definitely visit La King's Confectionery, every local and tourist will tell you the same thing, and if you can sit through the wait to get in it's well worth it. There are a lot of things to do on the beach as well, from dolphin tours to banana boat rides, theres enough to keep families entertained for a full week. Overall, as far as spring break destinations go, this is one of the best, especially if you're looking for a fun time but are still passed that college age group.