I know parts of Texas fairly well, but with the perspective of someone who grew up elsewhere.
Austin is a pretty good place to live. Decent scenery, mild winters, a lot of musical entertainment. The population is better educated and yes, more liberal than the rest of the state. Housing is relatively (for Tx) expensive unless you live "way out". Property taxes are obscene. Summers can be very hot and fairly humid even when it doesn't rain for a month at a time. The town doesn't "feel" overly large though traffic can be heavy at times...it just depends. Lots of water if you like to boat or fish. Though fairly diverse, it is still Texas and by that I mean an underlying culture of God, Guns, Football, and Bar-b-Q. If none of these things fascinate you...well, you get my drift.
Dallas is bigger and more "Texan". Money oriented. Not noted for it's natural beauty. Big Bugs. Still, if you like big cities you could do worse.
Houston is rougher, bigger and a very distant third IMO.
That's my quick (not so balanced) take