If you are registered with the district government as having your permanent address in an apartment in central Budapest,
you can get an annual parking permit from the district government for about HUF 2,000.
This is a very good price and is valid for the entire district. For example, I live near the Synagogue in the 7th district and I can park in this segment from Deak-ter all the way up to the City Park (Varosliget).
The backdraw is that if you rent a place, many homeowners will not give their consent for you to register in the apartment because they are afraid that
in something happens they will not be able to make you vacate the premises. Plus, if the rental agreement is filed with the government, they would have to
pay taxes on the rent. So even if you live in the apartment, in many cases you cannot have a parking permit.
There are exceptions to using the permits, of course. I cannot park on Karoly korut and Nagykorut, the two busiest streets in the district. Not that I could ever find a parking spot there, so it makes no big difference.
The 7th district is shaped like a slice of pizza and I drive up and down this pizza slice, parking my car the closest to the spot I need to go. I learned to go to restaurants and shops that are in the district so I
don't have to pay for parking. It makes my existence in Budapest very two dimensional, limiting my activity to this pizza slice and its immediate vicinity that can be reached from a free parking spot.