The video where he is holding his shoe is at the courthouse parking garage at 5th and King. That's why he interacted with courthouse employees (the Court address is 500 King St) I've been there several times. The way it works, you get a ticket on the way in. When you are leaving, you put your parking ticket into the machine and it tells you the amount, which you pay (I have always used credit card), and then you have 10 minutes to get to your car and exit.
And yes, Colonial has parking areas all over the region.
You were asking about the DoubleTree report. Philly.com (Philly Inquirer/Daily News) and other news outlets were reporting on Jan 5 that his car was found at the DoubleTree. For example, here's Will Bunch's report, which states: "Authorities said that Wheeler's car turned up later at a different parking lot, at the DoubleTree Hotel in Wilmington."
Hope this info helps!
And recall that he’d been at the courthouse earlier in the month, so perhaps that’s why his labored thinking had him go there.