If you are serious about going into the city, I definitely wouldn't take the L and take a cab instead. All of this is also heavily dependent on what time of the day you'll be arriving and departing ORD. If either the trip from or to the airport is likely to be around rush hour, then I'd stay put at the Sky Club. However, if it's middle of the day or late at night, then I say you go for it. There's so much good food in Chicago it seems impossible to make a specific recommendation but my personal favorite is Cafe Ba-ba-reeba for tapas in Lincoln Park (Halsted & Division).

Have a safe trip.