The current green-domed version - housing several museums with interesting exhibitions - is a post 1945 reconstruction. But down below are the remnants of several older palaces, which you can see for yourself if you go into the lower floors of the Budapest History Museum (in the courtyard at the back). Still, for most people, tha major attraction of Castle Hill is the Matthias church, which is abundantly decorated inside anside and out. The current neo-Gothicchurch was constructed at the end of the 19th century in an effort to build a church as it could have stood when King Matthias married there in the late 15th century (though nobody knows what that church looked like exactly). The romantic Fisherman's Bastion at its foot offers a wonderful view over the Danube and Pest. The rest of Castle Hill is dotted with cozy little streets with colorful facades, and beautiful porticos and inner courtyards. There are a multitude of restaurants, cafés, and art galleries. The outer ramparts and promenades offer more views over the Buda hills beyond. At the foot of the western wall of Castle Hill, you'll find the entrance to the Hospital in the Rock, which gives a unique glimpse into the system of caves and tunnels below. And you might want to see the changing of the guard in front of the presindental palace (besides the funicular train station), daily at noon.
Buda Castle district
Buda Castle - Grand Budapest Collection