Oleg his apartment is on a very nice and practical location for exploring Budapest. You will be in the center of Old Town, and visiting Lesser Town is only a 30 minutes walk. The apartment is not fancy, but has all the basics you need for a pleasant stay.
There is a very good Czech restaurant in the cellar of the same building, which is not just recommended by Oleg because it's close, for us it was also one of the better Czech traditional food experiences we had.
Please note that the apartment is on the 4th floor, and only reachable by staircase. The floors are pretty high, so it is quite a climb after a long day of walking and sightseeing.