It's not a hole in the wall place, but the first time I was in Budapest many years ago, we went to Restaurant Rosenstein. I think it's somewhat well known. My brother in law got the goulash. It was quite authentic and I recall they asked if he wanted hot pepper with it. Thinking he can handle spicy food he ma mistake of shoveling some onto the goulash before sampling it . Fortunately I tried a bite before that and it was delicious. I can also recommend the roast goose there, it made me love goose.

I've also found that I really like the "goulash soup" that is served in Hungary, but I've also found in the Czech Republic, Slovakia, and Austria. Basically all the same flavors, but in soup form. I assume cheaper and less labor intensive to make, but not as heavy and quite good. It's not goulash, but that doesn't mean we can't like it for what it is. May only be available in the more tourist-friendly restaurants.