The closest and probably least crowded option will likely be Lake Somerville. It is pretty good for your basic camping activities such as fishing, swimming, and hiking.
I do slightly prefer Huntsville SP over Lake Somerville, just a bit more scenic and varied to me, plus you can rent canoes to paddle around the lake. As mentioned, it might be more likely to be filled up on nice weekends due to it's proximity to Houston.
My favorite park in the area is Brazos Bend SP. Only about an hour's drive further than the others, about two hours from B/CS. Also near Houston, so it could be hard to get into on short notice. One of it's main draws is the alligators, of which there are plenty. Kids always get a thrill out of seeing them, whether from a distance or up close, and you can often get pretty close. Just be sure to keep your distance and don't harass them. I am pretty partial to Brazos Bend as my hobby is photography, and there is plenty to photograph there, especially wildlife. People do fish there as well, as long as you respect the presence of the alligators.
Never know what you might catch at Brazos Bend.
Crawfish seems to be on everything's diet. There are some big ones there, too.
It would be a good idea to check for availability and reserve a spot ahead of time for the more popular parks. You can do that on the
TPWD website.