I lived at the corner of Sheridan and Wellington in Lakeview 2 years ago in a large 1925 building. I had a smaller studio (650 sq ft) and paid $825 a month. However, I got to watch the sun rise over Lake Michigan every morning from a corner apartment with lots of light.
If you are just fine with no view, it gets cheaper.
Here are a few listings in locations I would recommend:
Great location, only a block from the Red and Brown line El stop
http://classifieds.chicagoreader.com...d=oid%3A253313
Fantastic location, a quiet street in the best section of Lakeview. You will love the access to the lake and the park. A block east and you have busses downtown, a half mile west and you have the train to downtown
http://classifieds.chicagoreader.com...d=oid%3A369594
A friend of mine lives in this building and he really likes it. The bedroom is actually a loft over the living area. The location is very good as well. Across the street from the Briar St theatre (Blue Man Group)
http://classifieds.chicagoreader.com...d=oid%3A354918
Another quiet street in the best section of Lakeview. I don't like the apartment finding services, but they may be worth it for someone new to the city
http://classifieds.chicagoreader.com...d=oid%3A123025