The restaurant in the Hilton is actually not bad at all. Once you leave the hotel and turn left to the square there also a few others but remember that they will be more touristy just because of the location but very easily walked to.

The entire castle area is a bit isolated in regards to walking but if you are willing to take a taxi or try mass transit then the city is within easy reach. A great area is around the octagon metro station with a few side streets packed with all sorts of restaurants