Hi
Parking in and around the university is very limited. Unfortunately on-campus parking is for staff and visitors only. There is a nearby multi-storey (Woodhouse Lane) but that is also £5 per day.
The majority of students who live in Leeds and have a car will still leave their car at home and walk/bus to campus. You could park in the student area of Hyde Park and walk the 10minutes to campus, I know that's what many staff members do! Any parking less than 5 minutes walk from campus is restricted to residents only or short stay (2 hours or less).
I'd strongly recommend commuting to Leeds via train for days when you are in lectures on campus, but I can see that the benefit of having your own transport on days when you are on placement will also be beneficial.
I hope that helps,
Amanda