My experience in Budapest earlier this year (2018) was that cards are accepted very widely and contactless payment also works. The funicular up to the castle takes cards but I did not try other public transport. I did find one restaurant slightly out of the way where card payment was not available but they took euros. I suggest you ask before ordering in restaurants just in case.

My experience in Budapest earlier this year (2018) was that cards are accepted very widely and contactless payment also works. The funicular up to the castle takes cards but I did not try other public transport. I did find one restaurant slightly out of the way where card payment was not available but they took euros. I suggest you ask before ordering in restaurants just in case. The Dohány Street Synagogue takes cards as well.

Edited to include information from helpful comment from Márton Molnár that public transport also takes cards.