What is parking like at UT Professional Building?

I have an appointment tomorrow at 6410 Fannin Street but I've never been there and I'm worried that no one answers my call tomorrow morning and I can't find any parking info on their website. I was wondering if parking is free there, and where/how? I thought of taking a park and ride on the red line if parking is not free (I've never done that before so it would be my first time navigating around public transportation). I could pay for parking but I'd rather not because I'm preparing a large bill from this doctor's visit…

Thank you in advance. You guys are my last resort…nobody I know has been to this clinic office before so any information would be great.