there is no cheap option in the city center of Budapest, so it is mostly parking houses that are expensive or parking lots of different hotels or shopping malls. You could check with West End City Center which is a big mall quite centrally where you can park. Another option is the Arena Plaza which might be a good second option.
But, if you want a much cheaper option then to park at Köki Terminal (where you can leave your car for days for a little fee), and then travel by metro or something from there to your hotel seems to be one of the best options to me.
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