Once in a while someone asks me to recommend places in Budapest,
so instead of writing them every time again, let me list them here and then
I can point them to this site.
Recommendations in Budapest
I guess it will be difficult to recommend only 2-3 places so here is a longer list with some comments.
Váci utca is the city center but it is very touristic
Vár (the castle) is romantic.
There is a nice pub/coffee shop area in the city in Jókai tér (Jokai square)
next to the Octogon which can be reached using the M1 metro line or by tram 4 or 6
Opera on Andrássy út
Vajda Hunyad Vára (next to Heroes square on the M1 track) a nice
romantic place for a walk.
in the winter I think you can rent ice skates there.