I don't know what your budget amount is, but I have visited the Brownsville area a few times and find it a great place to live. You are near Mexico if you like to travel there. The birding areas are considered hot spots in America. The weather is fairly nice.
Lake Texoma in north central Texas is a great retirement area. There is lots to do, and the cost of living is very reasonable for the activities and scenery offered.
Kerrville, TX is a great place to retire to, especially if you are a veteran. Everything you possibly need is there (including a VA hospital) at reasonable prices.