I would choose Baylor out of the bunch but all 3 are good programs. UIC is the most academic, while Baylor & UTSW are known more for their hands-on training. Of the group I think Baylor has the best combination of clinical & surgical volume while having enough name recognition to make you competitive for any fellowship.
I second that. Having been a resident at Baylor, I can honestly say I would go there again in a heartbeat. You do work hard but I feel i've been trained incredibly well both clinically and surgically. Simply because of the surgical volume (my class graduated with an average of 230 phacos (from run of the mill to complex traumatic zonular loss/uveitics) and we got to do a ton of other surgeries from tons of trabs/tubes, plastics/DCR, etc. etc.). There really was a tremendous breadth and exposure. We have a great mix of autonomy and supervision. All our surgical cases is staffed (by attendings!) which really says a lot and makes you such a better surgeon (which is not the case at a lot of counties). Not to mention the pathology that we get to see since we have a VA, a county (with tons of end stage pathologies being close to central america and the immigrants that come through Houston) as well as seeing both hospital surgical centers as well as our own ASC.
My class matched extremely well for fellowship. Two people went glaucoma Bascom and UCSF (prior years Bascom), Two people went retina Beaumont and Iowa (prior years went Emory and Casey), one went cornea to stayed at Baylor (the years before went UC Davis and Duke), and one went comprehensive.