This is the best downtown area for private walking in Budapest. The hostel is right by the Synagogue (see at http://en.wikipedia.org/wiki/Doh%C3%A1ny_Street_Synagogue, http://www.budapest-tourist-guide.com/budapest-great-synagogue.html) and the famous Astoria square.
If you walk down west direction any street in 10 min. you will find yourself at Danube river where is the best view to Buda (Buda castle, Gellért hill) and one of the best views of any of the Europe towns (you can see Buda castle and Gellért hill from some of our rooms as well ;)
If you walk by chance north from the hostel in 10 min. you may find your self by the biggest Hungarian church, the enormous catholic Bazilca. Walk more 6-7 min. north-west direction: you will find yourself by the Hungarian Parliament: obviously the most imposing building of Budapest.
If you dare to go south on the Kárly körút (your street where the hostel is) in 10 min. walk you will find the Hungarian National museum. In 2 min. walk form the museum look for Rádai str. there you will find more fashionable cafes and restaurants with live music from time to time.
North, a little bit north-east direction you may stumble in few minutes in the National opera house, the most famous street of Budapest: Andrássy avenue and a bit upper, the full of restaurants Liszt Ferenc tér. Some good night clubs can be found also in Nagymező str., which is very close to the Opera house.
The rest we leave for you to explore….