Go east to Florida is my advice. Being a Florida person stuck in the Houston area I can tell you that there isn't a nice beach here and the weather sucks, today it's not going to hit 55. Port A isn't going to get to 60 today either. I've been to a bunch of beaches here in TX and none have nice water or amenities or even compare to the most marginal beaches in FL.
Hit Ft Desoto for a week then head down to the Glades...you will have a blast with some great people (good luck finding great people in texas), great weather, great beaches and great scenery.