I'm an MSIV at UTMB, also happen to be in the Houston track but I did an AI at Galveston so I'm actually reasonably familiar with UTH, BCM, and UTMB when it comes to the IM residencies (regarding UTH and BCM my knowledge is limited to the overlap I had with them at St. Luke's). I am not particularly likely to stay at this program but I am a very strong candidate and I will rank UTMB (I have other geographical preferences)
UTMB was reshaped by the storm but I am not sure that it would be accurate to describe the program as weakened. For some convoluted financial/legal insurance reason there are large parts of the hospital that are still not repaired (including the first floor), but generally the functions of these areas have simply been permanently relocated. There is extensive construction occurring and in the works soon as well, which may be part of the reason for that.
There was a lot of realignment of faculty peri-Ike and many great folks left but the IM program is actually in much better shape financially and patient-load wise than it was in the year or two preceding the storm. According to Dr. Goodgame, the program is actually on pace for the best year in 4 years from a research funding perspective (Ike was 2 years ago). This trend is only going to improve. The storm appears to have forced the school to reevaluate its approach and, since Goodgame came just before the storm, it seems to have allowed him to rebuild it more soundly with a stronger emphasis on teaching, diversity of patient experience (exposure to world-class research facilities and private medical opportunities at TMC, a stronger emphasis on EBM training, etc.). The camaraderie of the program is also very good and you get the feeling it is a very laid-back program (good for some people, maybe not for others).
Faculty at UTMB are strong--not amazing, but consistently strong. I can say from personal experience that they are generally comparable to the faculty at Baylor, although I would suspect that Baylor might have more faculty in the "awesome" category than UTMB. I can only speak based on my month with occasional lectures, etc. from 3-4 faculty at SLH. The pathology from TDC is awesome. Dr. Goodgame is great, not just for GI, but meet the guy and you'll see; he knows his stuff all around and he is a very hands-on PD (in a good way). You just get the impression in meeting with him that the program is in good shape and will only get better. Again, you should meet the guy. The residents all seem to think he's some type of Jesus/Osler hybrid. Dr. Karnath is also a fantastic doctor and wonderful educator. He does a board review series for residents that is great and is always on the wards. Good research is also very easy to get into at UTMB.
My impression of Baylor's program was also mostly favorable. The residents were very sharp and interested in teaching. The same for the attendings. I do not have any information on the rumored financial insecurity of the institution, it may or may not be a problem, if I were you I would not worry about it too much. Research opportunities abound here as well.
UTH I don't want to bash, but the month I spent with an intern and attending (and I can corroborate my experience with that of a few colleagues) was terrible. This is anecdotal experience and, unlike BCM, does not include their upper-levels or didactic opportunities, so take it with a grain of salt. But I have not met a single example of such uncommitted-to-teaching, poor examples of attending physicians at UTMB ever in all of my time there. And I know of two such attendings. Additionally, the intern I worked with, when asked about the program, kinda shrugged like "it's not that great but oh well". He said many residents are unhappy with it. Again, this is an anecdote and I would not be surprised if the opportunities for great experiences exist in the UTH IM program, but that has been my experience. I do not know much about research opps, but I suspect, beingin the TMC, that good ones exist. I am not applying there.
So, in summary, UTMB is solid to good (particularly if you are a laid-back individual) and will see sustained improvement throughout your time there, BCM may be as good as its reputation (very good/excellent) with a bonus if you're especially into the sink or swim model of education, and UTH is probably not too great an option, but it'll get you where you want to go if you're sure you wanna go there. If you prefer the island to Houston or vice versa, you might have your answer (for me, who has lived in both, give me the island, but many would disagree).
All of this is my two cents.