FYI - I was checking CTA last night & from midway, you get off @ state & lake and it's about 1/2 mile walk to the Sheraton (or you can take the bus from the Van Buren stop if you really want) and it's only $4 or so round trip  

 

Here's the link if you're coming/going from elsewhere (o'hare, etc)  Of course, if you're bringing a big bag you might be better off using the airport shuttles but it's up to you.   I'm attempting to pack lightly but we'll see how that goes... LOL