Yes, the hotel has it's own parking. It is a little tricky to go into the parking because the streets are very narrow and the entrance to the parking is quite difficult. Reserve the parking in advance because it is limited. Once you park your car, you may forget about it since everything to be visited is at walking distance.
You need to arrive to check in first so they will open for you the garage and tell you how to get in.
Parking is just outside of the hotel. I don't think they have garage but you can email and ask.
el aparcamiento está al lado del hotel.
Tha parador is about a 20 min walk from the centre, has free on site parking and cracking views of city.
Hotels at the Plaza Major are boutique in nature and very few on-site parking is available.
Get quick answers from Plaza Mayor staff and past visitors.