You can get up here on the bus, tuk tuk or the red tour buses. The views are staggering and you almost get a full 360 of Budapest. The citdel is on the top of Gelllert hills and has a cafe and a small museum and several small market stalls selling souvenirs.
There is also the Budapest Statue of Liberty
Its also free.
The only thing that spoiled ot for me was that there was a group of scammers - find the peanut - obviously hustlers with a convincer and others roping poor unsuspecting tourists in when all along its a con and he just hides the peanut in his hand. dont be fooled