We went a couple of years ago and loved it. It felt like a really young vibrant city, with that old Eastern European look - Old trains,
old trams, bullet holes in the buildings, etc.
You've got a couple of days, so a day on either side of the river should do it. When you go across to the other side, walk up to the Citadella
for the view. Then you're on the right side for the castle, museum, etc. I'd stay on the other side (Pest), so you're in amongst it, but I'd imagine that the hotels in the boozy area are noisy at night. The hotels were great value btw, compared with other big cities.
The beer's cheap, especially in the ruin pubs. If you want to pay a bit more, there's a cracking craft beer bar called the Marionett, down on the front by the Marriot Hotel.
The food was great, especially if you love paprika.
If you're flying in, you can get a public bus and then the metro, which drops you in the centre of town. It's really cheap.
Have fun.