Most of the city of Houston is pretty liberal. Some areas aren't, and gerrymandering gives them too much power (in my opinion as someone who leans more towards the left). All in all, though, Houston votes Democrat. It's also extremely diverse. I love the city of Houston. The suburbs, though, are very "Texas" and tend to be much more conservative. I went to high school in one and hated it. I don't have much experience with Dallas, but I know the city tends to vote Dem. I bet their suburbs are as conservative or more so than Houston's, though. When you look at maps showing how people vote, Dallas, Houston, San Antonio, Austin and the area near the Mexico border are always dots of blue in a sea of red. Those bigger cities are generally a much more liberal feel. I'd say Austin is maybe the most consistently liberal though. But if you ended up working in Dallas or Houston, I think you'd feel pretty at home. Especially in Houston. But Austinites and Houstonians are just made to hate Dallas so I'm biased.
Oh ya, it's pretty close. I'd say Sabina is maybe a 15-20 minute walk to the law school. I'm pretty sure there'd be sidewalks most of if not the whole way too. I also think it's a pretty short walk to one of the UT shuttle stops.