I'll start from how you get there...if you love walking it's a nice walking distace from pest and then to go up you can take the carts which are a bit pricy (like evey tourist attraction), we took it only one way and when we went down the stairs we discovered how small of a distance it is, so it is possible to go up the stairs easily, there's also public transport just ask at your residance's reception and they will tell you what to take. For the castle itself you can go inside there are museums/exhibitions which I didn't go to so can't review, but you can go around the castle itself, there are beautiful statues and gardens and different constructions.