The general Medical Center area south of down town Houston includes Rice University, Herman Park, the Houston Zoo and some of the most expensive real estate in the city.
That being said, there is some crime everywhere. Realtors cannot comment on crime rates because we do not keep any of that data. It would be a "guess" if we did say anything. Check out this web site created by the Houston Police Dept that is real time updating every few minutes. http://mycity.houstontx.gov/crime/ Also speak to people that live there, maybe the local police officer on patrol. Hopefully this will get you the information your looking for.
If we can assist you in finding your new home, please let us know.