Stay away from north side, it's really rough out there and you'll probably get shot.
South side is probably the most normal part of town there is (and is also where i live! ha). Living arrangements here span the spectrum of houses that look like god damn castles (see Lafayette square) to crowded townhouses where all the immigrants come to live. Probably your go to if your not going to live out in the neighboring counties since you said apartment and not house.
East side is pretty ? ? ? non existent. lots of abandoned buildings and empty pavement.
West end is where all the rich white people live if they don't live in Lafayette square. If your super rich, look here.
And downtown is where all the tourist stuff is. Lots of fun, defiantly take a look around, but as far as living, it's mostly just hotels and the like, but i'm sure there are a few high rise apartment buildings trying to pretend their in Chicago, but those are probably as expensive as places in West End.
Also everybody here says their from ""st louis"" but most people live out in the counties see: Fenton, Brentwood, Ellisville. Good for hosue hunting, not so much for a young collage grad. You'd get bored out there unless you grew up in the subburbs, which is exactly what the counties are.
Also you should get a place near or inside southside because~~!
-It's also nearby where lots of cool stuff like the Science Center, the St.Louis Zoo, the botanical gardens, The Muny, the butterfly house, The Fox theater ( a must see, absolutely stunning) Forest park, the city museum and a bunch a other stuff. All these places are pretty spread out, but all the highway entrances and exits to get there are in southside.
Also there's a newly built ikea here so definitely check that out for some housewarming! Anyway just take a good look around, try to get back home before 10pm unless your in a group, and good luck! And stay away from north side.