Unless you want to leave the car alone for your entire stay, the usual free in and out privileges at valet park will likely trump the rate differential. The closest option that is not too far is the Millennium Park Garage. It is accessable from lower Stetson St. or from Columbus Drive. Getting there in your car from the Swissotel will be a challenge the first time, but it is a short walk. And if you park overnight it is not cheap.