EC Harris have an ofice in Budapest, on the corner of an ugly brown brick building on Kiraly u. They are big world wide, good reputation. Maybe too big for one apartment but try them anyway. In some cases I have found that if you drop into a big company like this, they will either know of someone or one of the surveyors will do it as a "nixer." I have to stress that I have never asked ECH to do anything like that, but just in general you can often get good advice free this way.
Surveying an individual apartment, as you may be aware, is not really of much value unless the entire building is surveyed, which would be very costly. Probably what you need is someone who can simply snag the apartment and ensure that the finishes meet the specification and that there are no outstanding issues. If you are already doing business with a management company, they probably have someone in house who can do this at a very small charge.