You can check out my blog posts here
But in summary:The Szechenyi baths is where all the locals hang out and is pretty cool to people watch on a Saturday morning
Food:
Gerbeaud Cafe - its expensive but was in every book based around Budapest
Great markets - upstairs has like a "fast food" stall
Koleves - traditional Hungarian food
M Restaurant - Translyvanian food
Klub Feszek - local club, kind like a an Aust RSL but better