The apartment itself is very nice, and in a great, Central location for exploring Budapest.
However, be sure to read the fine print! The check in is NOT at the address listed, but rather in a small office nearby. And that office closes at 6pm. If you arrive later than that, you have to call and arrange to meet someone, who can check you in. If you don't have cell service in Hungary, this could be a very complicated or costly endeavor! This seems to be the case for all the Budapest Holiday brands.
If you've got international calling, data, etc., on your mobile, this may not be a big deal... But if you're trying to get by without, I'd suggest paying a bit more and going to a more traditional hotel with a real check-in desk.