Vipeuup,
I parked my Z06 in the Union Square parking garage, as well as, a few others, notably the one across the street from the Metreon. I felt that it was safe.
I would suggest not taking your Viper. It may cause a little bit more attention and those parking stalls are not Viper friendly.
I have taken my Viper to the city, but have paid for "premium" (valet or up front) parking.
Warfang is right, I would not encourage it. If you did decide to park it there, you would be like what Viper Scot said, " I would't be able to relax with my car in one of the parking structures."