As was noted in some private emails, the Chicago Marathon is scheduled for Oct 9. Consequently, you should make your travel plans as soon as possible, especially your housing plans.
I went with AirBnb again this year and landed a spot just one block from the Sheridan station on the Red Line. I'm driving this year. Some places in Chicago require permits to park. Usually the host can obtain guest parking permits. In the ward where my host resides, these are just $8 for 15 daily passes, so the parking is really just about 50 cents a day. I told my host to buy the 15 day option and just keep the rest for other guests. I'll probably just park the car and use mass transit, but will be driving to and from Chicago.
AirBnb's search map now shows the CTA stops for both train and bus fairly well. You can focus on those locations when searching for a place to stay. I had a couple of declines this year due to scheduling issues.
Because you may be staying in someone's home, I generally contact the host before trying to make a reservation and inform them that I'm transgender. I'm not saying you have to, I just feel more comfortable doing so. I don't want a host to be surprised and then uncomfortable. That point aside, I've found that contacting the host before attempting a reservation usually gets you a better chance at having your request accepted in general.
Hotels are filling fast and other options like AirBnb may start doing so as well.