Planning a trip to Chicago in September. Have location questions any advice would be awesome....?

I'm planning a trip to Chicago this September. I'm coming into union station from Buffalo. I want to visit Lincoln Park Zoo and the Old Town neighborhood, as well as the sears tower, botanical gardens, etc. Where would the best location be for a hotel? I'm looking for relatively cheap ($100-$125 per night) and something that's close to union station, but also close to attractions listed. Is there somewhere in the middle? Also, any recommendations on sights to see that weren't listed? Thanks! :-)