I used to work in Budapest around the turn of the century. Folks above have it covered
+1 for:
szczesny baths
gellert baths
castle
river cruise
If these places are still going, they are worth going to:
Old Man’s Music Pub – as the name implies, live music most nights of the week.
Fausto Italian – not cheap, but super quality.
Listz Ferenc Ter (Frans Listz Square) had outdoor eateries & a nice vibe, just round the corner from Oktagon.
In March you might still have crappy weather, it might be ok. Snow should be well gone, but roads might still be filthy, take some sturdy shoes.
egészségedre