Some suggestions

ibis Budapest Castle Hill 
Address: Krisztina krt. 41–43.

Buda Castle Hotel 
Address: Úri u. 39., 1014 Budapest

Gold Hotel Budapest 
Address: Hegyalja út 14, 1016 Budapest

Hotel Castle Garden 
Address: Lovas út 41, 1012 Budapest

Mercure Budapest Castle Hill 
Address: Krisztina krt. 41–43.