The Central West End is an ideal place to live if you'll be working on the medical campus. There are a lot of great places to live, and it's a very friendly, "hip" community (as hip as medical and graduate students can be, at least). It's a bit on the pricier end, but it's possible to get a reasonable 1-bedroom for $700 (everything except cable/internet).
As for crime, the big issue in St. Louis is with car break-ins. If you do have a car, I would highly recommend garage parking or at least a gated lot. Don't ever leave any valuables in sight. I've never personally had my car broken into (not that there's anything they could steal anyway, though it is a nice newer car), but it's happened to at least 2 people I know in the 1 year I've been here.
I've never heard of anybody getting mugged or anything like that. I feel safe walking home at night; however, I am a 6'2" guy. I'd probably feel less safe as a girl. The police on campus have a system where you can call them if you feel unsafe walking home and they'll give you a ride anywhere in the CWE at any time of the night. Sometimes people just use it when they don't feel like walking back after a long night of studying .
As for the queer-friendly comment...it's not San Francisco, but it's about as queer-friendly as you're going to find in the midwest. It's a typical liberal university community. I have never seen any sort of gay bashing. It's not like Missouri is the Deep South