It does depend on where you want to go, as well as what time of year...

I've cycled the ACA route from El Paso across to LA. I've also gone from Brownsville to Dallas - and just over Christmas cycled from Brownsville to Laredo to San Antonio to Austin. A few more general thoughts:

- Texas west of the Pecos River is much more of the West Texas, with dry and wide open spaces. I believe it has a certain beauty and so enjoyed that ride from El Paso further East. However, also a bit of acquired taste and Alan Guo recently decided to bail on wide open spaces (of NM/AZ) after riding through it.
- If you are looking for a bigger mix of occasional cities, then starting in Brownsville and coming up the center and going via Laredo, San Antonio, Austin, Waco, etc will give you a somewhat different slice.
- The Panhandle is a bit cold now, but a different type of wide space and just slightly cooler on shoulder seasons
- Texas Hill Country great place to go, and upcoming Texas Hell Week in middle of March is a great time to visit and explore that area

I just moved here two and a half years ago, but have been making a point of cycling to different state parks within riding distance of Austin. Not a long tour but right now is good time to explore (July/August just a bit too hot for me - I'd rather escape elsewhere).