Well, I mean, some of the hospitals ARE skyscrapers.
Houston is weird because of its lack of zoning (well, it's weird for lots of reasons, but that's one of them). This contributed to the fact that there is no single "skyline" here.
Certainly downtown has prominent towers, but there are also towers in the "Galleria Area", in the Greenway area, and of course in the Medical Center.
However, my actual procedure was done in a fairly short (4 or 5 story) dedicated orthopedic facility not in any of those areas, but associated with Memorial Herman.
A place that has hospitals the size of skyscrapers.