Must see, and stay for at leat 5 days
I have visited Budapest a few times earlier, but always for a day or two. If you really want to get a full experience, stay for a few days. Lots of interesting museums to visit, Terror museum especially. Visit the Hero's square, take the free walking tours, the guides are amazing, and know so much about the history of Budapest. Also, must see - ruin pubs. Fantastic places, cheap beer, great music. Budapest is a place to visit, lots of things to see and do, so pack your bags and come. :)
Insider Tip:Ask at a hostel/hotel for a good place to eat. And avoid eating near the Vacci street, the prices are much higher there.