Aaron,
If it really means a lot to you to avoid valet parking, try finding a Municipal/public parking lot somewhere in Chicago. I live in NYC more than half my time and have a dedicated park-it-yourself spot for my apartment, but before I lived in New York and had to drive in for events and evenings, I'd either find a good un-metered street spot OR park in lots that were self-park like at Lincoln Center, or, before 9/11, in Police headquarters. Somewhere in Chicago is a self-park, and you seem determined enough to find it.

Alex

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1983 300D (parked for four years)
2012 VW Sportwagen TDI Manual
2001 Miata SE
1962 Chevrolet Corvair Rampside