Of course, I found a door I like!
St. Anne Church, on the Buda side.
A market hall (VI. Vásárcsarnok) in Buda. We initially thought this was the Great Market Hall, but that one is on the Pest side.
Inside the Buda market hall.
Most of the following buildings are in Pest, specifically on or around Andrássy Út.
Gresham Palace, now home to the Four Seasons Hotel.
The House of Terror, a museum dedicated to exposing both the Arrow Party (Nazi) and ÁVH (Soviet) parties of Hungary. Both chose this building as their headquarters, and the museum takes you through four floors of exhibits and information. We found a lot of the exhibits only give Magyar (Hungarian) explanations, although papers are available in English in each room. (Even the official website doesn't want to translate, despite having an English button available.) About half of the shown videos and interviews are subtitled. It's a little disappointing to not be able to understand the entire exhibit, and I found myself comparing it unfavorably to the phenomenally well-done Oskar Schindler's Factory Museum in Krakow.
Paul would like a cupola on top of a house like that. I think it looks like a steam-punk submarine.
Buildings in Buda.
The Budapest University of Technology and Economics sits on the Buda side of the Danube directly across from The Whale. This is just the center part of the riverside facade.
The Central European Time building, also known as "The Whale." CET is a Magyar synonym for whale, befitting the organic shape of the glass ceiling. The "tail" of the building sits above two old warehouses, on the Pest side of the Danube.
Hotel Gellert, on the Buda side at the end of the Liberty Bridge.