There is street parking which, depending on the time of year (like summer), might be more of a challenge to find than at others. But the hotel is worth it. Just lovely.
There is a lot of parking places in 50 meters, just on the square. And in 300 meters, before paid zone.
Just street side that I am aware off
yes, the hotel offers car parking (18 or 20 euros a day)
There is a nearby public car park that costs about 20 euros a day I think but I don't believe the hotel has its own guest parking. However it is really central, the taxis were cheap compared to other parts of Europe and for one day we used the tourist sightseeing bus which has a 24 hour ticket so you can hop on and off at will.
Get an answer from Hotel Gutenbergs staff and past guests.