Drive it off the nearest cliff, AAAAAARRRRRGGGGGHHHH
Jejejeje, as someone who has a car here, does not want one and is about to buy a new one within a few months

(ena, my gal, needs it to get to work and back), I can tell ya that in the city center and many other neighborhoods, free parking is a nightmare! (except in August when the city is pretty empty).
We park our car in the street and can always find space about a 10-15 minute walk from home and sometimes we get lucky and find a spot rigth around the corner.
Private garages are rented out by their owners but it would be hard for one month since often people are on waiting lists for years to get a rental

Price depends on location, in the center (around Puerta del Sol) of the city prices run about 100-150 Euros/month.
Public garages are an option and for one month it would not be bad (price depends on the area you want to rent in).
What area are you staying in?
Saludos,
jer...