It is free to park your car by Savoya Park, both on the outdoor parking lot in front of OBI, Aldi, Rossman, and also beneath those buildings, and there is a similar free parking lot beneath Auchan by SAvoya Park. I would be hesitant leaving my car there for a very long period, but for a couple of days, I probably wouldn’t worry a lot.
From there, you can travel by tram to the city center of Budapest, so it is actually a quite nice place and good solution if you want free parking in Budapest while doing a day of sightseeing or so.
More information on parking at https://www.hungarybudapestguide.com/free-parking-in-budapest/