I lived in the South Loop my first year, and while affordable and close to everything, didn't feel safe out at night.
I moved to Lakeview and would recommend it to anyone. Buses to downtown are at my doorstep, tons of cabs, I'm a block from more stores than you could fit in a mall, and there's 5 or 6 bars less than 5min walking in any direction. You can get a decent one bedroom for $900-1200, depending on the amenities included. Street parking is possible, and I would try it first because rental parking is $150-250/month or $30,000 deeded.
When I first moved here I sold my car for extra cash while adjusting to city living as a new grad. I have to say I bought a car after my first year here and live having the flexibility. I have friends who've lived here 6-7 years and never bought a car. It's easily a savings of $5,000-$6,000 a year.
I agree with other posters that you should research the neighborhoods around your top choice hospitals. The culture of the neighborhoods around hospitals is impacted by the high numbers of healthcare professionals in the area (i.e., hospital bars in EVERY neighborhood). Keep in mind that some areas are far safer than others. The City of Chicago website has an excellent crime survellience tool that can show you the prevalence of crime and the type of crime in the neighborhood, right down to the street adress. http://gis.chicagopolice.org
Like these other RNs, I'm slightly crazed about home/rental research. I think you pretty much have to be to find great places to live in the city. PM me if you decide to move to Lakeview!