Chicago neighborhoods are definitely important to know, though I'll add that the area west of the medical center is really not as bad as people make it out to be - in fact, I've heard of more crime in the area east of the hospital (Little Italy) than west (Tri-Taylor). Lots of med students live in both of these areas and they make for a really convenient place to live, at least for M1 and M2.
Living in Lincoln Park is probably not a worthwhile use of your money. If you don't want to live in Little Italy or Tri-Taylor, there are plenty of neighborhoods that are a bit more trendy, not as far as Lincoln Park and certainly not as expensive. These include Ukrainian Village and Logan Square.
Again, I'm a current M2 at UIC. Here's another offer to answer questions by PM (though I don't check the thread regularly, so don't bother asking them here). Feel free to give me questions about Chicago, school, activities, whatever. You can check out my MDApps for more info about me.