How about Houston? Several people from my barn (just south of Houston, about 20 minutes from downtown) actually just went to the beach for trailrides recently.
Lots of opportunities (at all levels) for showing and clinics in h/j, dressage, and eventing. Probably western, too, I just don't know the people doing it, lol. Also lots of barns to just board your horse until you have time to go hang out with him.
Housing is realtively inexpensive, employment is good (especially compared to some areas of the US), and there is no state income tax. Lots of horsey and non-horsey stuff to do. People come here from all over the world (most in the oil industry) - I work with people from the UK, South Africa, Venezuela, Costa RIca, India, China, Poland, and Canada.
There are several good local colleges. My instructor/BO was a psych professor at Rice (and coached their equestrian team for a while after she set up her barn), and there are several campuses of the U of Houston. College Station (A&M) is a bit of a hike, but I've gone past it to get to some clinics, lol. And there's something in Galveston, I think.
The main drawback is the summer heat. It gets to the 90s fairly early in the year (April or early May) and stays there until Spetember or October. Yes, it also gets humid, but IME, the humidity was way worse in DC (It just didn't last for 6 months).
Just FYI, Houston was on my list of places I didn't want to even consider (as was Miami, Alaska, and Detroit for various reasons) but there was a job offer and I badly needed to get away from my old job. Moved here from upstate NY (Troy), and have survived 3 summers. lol Do NOT miss the snow, just the autumn leaves in the mountains.