We live near Midway and I tried in vain when the old $20/nt. bonus money offer was around to get a room so the kids could swim. I ended up going up to about $20/nt plus $20/nt. bonus money for a 3*, then 2.5* with no success. I suspect that rooms are pretty scarce around here and I've gotten much better deals near OakBrook, Downers Grove, Downtown Chicago, etc.
The hotels that are close to Midway are Hampton Inn, Courtyard, Comfort Suites, Holiday Inn Express, Four Points Sheraton and they offer free shuttles to Midway. Maybe you can check their rates individually and get a good deal.