I'm really not sure of what to recommend, but I'll put in a recommendation for Roscoe Village. It's nice and quiet, close to the El and buslines. I walked around the area today. A lot of nice little shops, laid back people, and a candy store that makes their own icecream. Well, I like it anyway. Also, a lot of small taverns and restaurants. I had a fun time there today. Although I will say that there were kids around, but they didn't annoy me, so they must not be that bad.
There are a lot of places for rent around there. The only price I saw though was for a 3-br and it was about $1600. So, not sure where that would leave a 1-br.
Greektown is also nice. My office is there and it's close to the Blue line and busses and right outside of the loop on the southside.
Stay away from Lakeview though..it's pretty crazy. Too goth/sex shop driven in the area I was in earlier this week. Not what you want I think.
If I find any other areas I'll let you know.