The best view of the city at night. Go there with your camera.
Use bus Nr 7 until Rudas Fürdő From there you may walk up on foot. That is a steep / exhausting walk. (700 meters)
! the very top of the mountain (where the statue is) is currently closed due to renovation. !
Europe's biggest and most beautiful Jewish church is very impressive even if you have just little time to check it from the outside. (There are also guided tours during daytime. it takes approximately 1,5 hour)
This is the most exquisite building the nation has erected.
Walk around it on the Pest side.
The best photos can be taken from the other side of the river in the afternoon (Lights come from the good direction). Use metro, go to Batthyány tér. From there it is the best to look.
Discover the party district:
The inner part of the VII. district is the party and fun district of the city. The main attractions are the ruin pubs. They are a national specialty. The story behind them is that after the country became democratic and the Soviet forces left Hungary, many buildings remained empty, also in the downtown. Young urban entrepreneurs converted them into special pubs and music places. Check at least one ruin pub. The first and most iconic is Szimpla kert. (VII. Kazinczy utca 14)
If you have a little more time:
Visit one of the city’s historic markets. The place where local people go is Hunyadi tér. The building is a bit run down inside, but still an architectural masterpiece
Eat there a : Lángos - cheap, delicious, nutritious, authentic market food.
You see how real Hungarians buy their ingredients for cooking.
The biggest and most beautiful thermal bath is Széchenyi. It has some open air and some indoor pools all set in a XIX-th century palace like building. Best to go there in the afternoon.
After the spa visit the Vajdahunyad castle on the opposite side of the street.
Then you can walk from Hősök tere way up on Andrássy avenue. Beautiful palaces all along the way.
Take comfy shoes.
Unicum is the most characteristic Hungarian spirit. Mr. Zwack invented this magnificent piece of wonder and ever since this distillery is in his family’s hand. Their history goes back to the Hapsburg empire. Visit their museum, which is not only interesting, but you can sample their products as well. A place that is not in the city guide books, but it is absolutely interesting.