Budapest Museums and other sight entries.

Not that I'm aware of...I always deal in the currency of the country I am in, or use a credit card. If you are concerned about dealing with an odd currency (as I think of forints or zlotys or korunas, for example) go to the Coinmill website and print out the wallet size currency converter https://coinmill.com/

At Szechenyi bath today there was a sign at the cash window that they do not accept Euro. Credit cards or Forints only there. Can't say I saw a similar sign at Gellert or Rudas, but it might be the same. Forint is the official currency of Hungary. You should make sure to have them available when making purchases with cash.

There are lots of ATMs around you can use to withdraw Forint. Just keeps you eyes open for ATMs as you move about. They are everywhere.

Just remembered...I also a a sign at the Matthias Church/Fishermans Bastion ticket window today that Euro are also not accepted there.

I believe the Parliament building and associated eating establishments post prices in forints AND Euros -- if you're willing to accept their exchange rate. Credit cards are the way to go (assuming, as mentioned above, that they are free of foreign-transaction-fees.)

Any reason you don't want to exchange your Euros? In Budapest we found many small exchange places that will give you a very good exchange rate and not charge you a fee. We changed Euros at them a couple of times when we were there.