Restricting your search for clinical psychology programs to one state, much less one city, is extemely tough. Something like 90 percent of clinical students have to train in another state because of the sheer competitivnes of the field/programs and the diversity of research interests that one can have. Its not a very viable option unless you have made yourself some kind of superstar in undergrad. Even then, it would be risky simply because of the statistics of the applicant to acceptance ratios in this field. I would get used to being at least somewhat geographically mobile in this field because you will have to move (probably out of the state you're in) for the pre-doc intership year. My, and everyone else's advice is going to be to get used to being more mobile if you want to pursue this field.
Texas also has alot of competitive programs, which doesn't help your situation any. Off the top of my head: Southern Methodist University, UT Southwestern Medical Center at Dallas, University of North Texas, Texas Tech, University of Texas-Austin, Sam Houston State (known for forensic stuff) University of Houston (known for neuropsych). As far as I know, all except North Texas offer remission and full funding. Oh, and I think there is an Argosy campus in Dallas, but you don't want to do that to yourself.
"Good psychology programs" are ones that are good for
you and
your interests. For example, no one would argue that Yale is a bad psych program. But would it be a good for
me? No, not at all. It explicitly wants to train academics (even though its a clinical program), Further, and probably more important, there is simply not alot of research going on there that I'm interested in. Im interested in aging and the neuropsychology of aging, so I looked at programs with people who are working/researching in that area when I was applying. People pick Ph.d programs for the faculty and how it matches with what they are interested in researching and pursuing while they are there. People get accpeted because they "match", and "fit" with a professor who is taking students. So....what are you interested in? And are there any profesors at the texas school doing that? Psy.D program dont have that model, so thats not so much of an issue, but I think there is only one Psy.D program in Texas. UT Southwestern, even though its a solid Ph.d program, also doesn't use a mentor model. But obvioulsy, you should be applying there for a reason, not just because its in texas. As with all programs you apply to, there should be some componet of the faculty or what opportunities are offered there that is driving your decision to apply there.