Does anyone drive a scooter to work in Houston's Medical Center, if so where do you park, and is there a fee?

I'm thinking about buying a scooter, but I don't see any other's parked at 6400 Fannin.Does anyone drive a scooter to work in Houston's Medical Center, if so where do you park, and is there a fee?
I drive to work on a Vino 125 in NW Houston, I see more scooters here every day. We just park anywhere a car would park, or split a spot if you have a scooter buddy.