Galveston Island Brewing is amazing. Its actually my top brewery in all of the Houston metropolitan area. Everything they've made tastes great and they actually make a plethora of different beer types instead of all ipa's.
I was actually just there yesterday and was great. In November they should have a couple of my favorites tapped: drunk dunkel and coastal christmas
Other than them, naked iguana is close to the strand and decent, I just try not to support them because they are very pro-cops and feds, which is not my jam.
Another beer recommendation (and whiskey) is beerfoot they have a great collection of local beers and an eclectic whiskey collection