Lots of places to try. I usually fish the surf or on the inshore waters. If you head east out of town on bluewater highway towards Galveston you will find all sorts of place to fish. Keep going a few miles and you will get to SLP ( San Louis Pass ), havent fished there but a lot of people talk about it.
This year we will be down in June and we decided to hire an inshore guide, so that might be something else you can look at.
When you get down there, just stop at one the bait shops and ask what has been hitting lately and where, most will be very helpful.
We went for the first time a few years ago and I feel in love with that place, this will be my 4 trip in 3 years and I wish I go more.
Here is the guide we hired, his name is Randal Groves.
http://www.grovesguide.com/