You can get crime data (as well as "calls for service" information - when someone calls the police, but not necessarily a crime) from the SAPD website - http://www.sanantonio.gov/sapd/indexcrime.asp
The home you speak of is located in the "North Substation" (in case you're looking at the map data).
You can also visit the North Substation at 13030 Jones Maltsberger or call them at 207-8126(V/TTY).
(In case you're wondering why Realtors always refer you to the SAPD, it all deals with liability for us...if we label a neighborhood as "good" and you think its rotten, we could be held liable. There are also potential Fair Housing issues when talking about neighborhoods. Its not that we don't want to help you find the best neighborhood, we just have to be careful not to frame any neighborhood a certain way. As well, the police are the experts when it comes to crime, so we leave it up to them.)
As for hospitals, Northeast Methodist is about 2.2 miles from the home - http://budurl.com/MapNEMethodist
There are various nursing homes nearby, here's a map for you - http://budurl.com/NursingHomes
Hope that helps! Any other questions, feel free to ask.