If you budget $800 a month you should be able to find some decent in Logan but definitely not anywhere closer to downtown. I lived in Logan, Wicker, and Lakeview and there's no way you could get me to live in Logan or Wicker over Lakeview again. Just doesn't compare in my mind. Everyone has their own flavor. I wouldn't be afraid to look off the blue line as its not hard to take a red or brown downtown to the blue line, or a bus west towards it.

Park Ridge is nice. Jeff park is cheap as well but not a lot going on out there except residential. Personally, I'd stay away from anywhere northwest of the Belmont stop. Not my cup of tea.