There is a municipal lot across the street from the Sheraton, which is a 5 to 10 minute walk from the Ritz. On the weekend, the rate is $5.00 for 24 hours. When my friend comes to visit for the weekend, he parks there late Friday night and then we move the car late Saturday night to a street with free parking on Sunday, so a pretty good deal.
The garage is off 16th street just past Race street. After crossing Race St., turn right on Spring St and the garage is right there; can't miss it as it has a big sign advertising the $5.00 weekend rate.