This question is posted in the GENERAL forum https://community.ricksteves.com/travel-forum/general-europe/advance-ticket-sales-883723d6-c25a-4ce0-9931-5b17d081cc19 so I thought I would post the answer here:
(P) Great Synagogue: buy at the door. absolutely no problem but be aware of the hours. http://www.greatsynagogue.hu/gallery_syn.html#4
(P) House of Terror: buy at the door. closed on Monday. http://www.terrorhaza.hu/hu
(P) Heroes' Square: FREE
(P) Vajdahunyad Castle: mostly free, but the Agriculture museum tickets (inside) you can buy at the door. http://www.vajdahunyadcastle.com/tickets-to-the-vajdahunyad-castle-budapest
(P) Holocaust Memorial Center: buy at the door, but be sure to leave a generous donation in the box inside.
(P) Hungarian National Museum; buy at the door http://hnm.hu/en
(P) Hungarian National Parliament: purchase on line in advance as soon as possible http://hungarianparliament.com/tours/
(P) Any theater tickets: purchase in at least 3 months in advance; better yet, the day they go on sale.
(P) Zoo; at the entrance http://www.zoobudapest.com/en
(P) Szechenyi Baths: in advance for convenience, or at the door. http://szechenyispabaths.com/