Congratulations on the offer!!! It's a great feeling of relief isn't it!
Henry Price has a few car parking spaces but not enough I don't think for all the students who want one
Lupton seems to have quite a few spaces (but parking near the university isn't easy, so driving into uni every day isn't necessarily the best plan - a lot of students don't get a car until they are in 3rd year and on placements because the public transport is good, and it only takes 25 mins to walk to Headingley from campus)
I'm not sure about other places to be honest, but the website does say for some "parking" and for some "limited parking" which probably gives you a good idea of where you will be able to park
http://www.leeds.ac.uk/accommodation/flats.htm