Parking is at a premium the closer you are to the clinic building so there is often a charge for parking. The room charge is steeper as well. That’s pretty normal in any city…the nearer the venue, the pricier the lodging.

Near the clinic, within easy walking distance, is the Hilton Garden Inn, the Kahler inn, Doubletree, Marriott Residence Inn, etc. We’ve always stayed nearby allowing us to walk so I don’t have first hand knowledge of hotels further out.
There may be other members popping in with ideas for you with their experiences at favorite hotels. Again, if you’re not sure of a hotel, contact the concierge with the information I posted earlier. It’s a free service and they’re super helpful.
I’ll look for some ideas for you.
Is your first appointment Monday Morning?