cheap hotels are a very short cab ride or shuttle ride away.
Shuttles require a 10-15 minute walk to get to the pickup area.. and a bit confusing. AND then they only come on their regular basis (every 30 minutes normally). I am not sure at 1am if you should call them FIRST then wait or what. Shuttles are NOT the best option.
Cabs. Yea.. maybe some cabs around. But they want LONG runs since they have been sitting around all night waiting for a run. They may not be too happy at a $10 fare to the Marriott hotel!
Limo. Expensive but they WILL be there. Cannot suggest anything .. try a search.
Not sure that I have a good suggestion! Ihave friends I call in ORD when stranded .. they work out the best! I agree 4 hours sleep will not be fun.
I'd try the Hilton AT the airport. NOT cheap.. but RIGHT THERE and then you are on expense account... and can take the money out of the secretaries bonus!