You can choose the usual tourist attractions, start on the Buda side, walk the castle, cross on the chain bridge, see the parliament, walk Andrassy street and the Hero’s square and the nearby park. Safe choice. Here are a few hidden gems you might like: try Rudas Spa, some parts are 450 years old and you can have a jacuzzi over the river. There are nigh schedule on Friday and Saturday. This is better than Szechenyi in my opinion. Try the pinball museum. Also open till late and a nice activity after a long walking session. Take the Libegő to János hill and enjoy the view above the city. Party at a Ruin pub, I think Morissons 2 is an experience. If you still want more take a boat trip on the Danube to Visegrad. It will be a full day, but amazing historic place there and nice nature.