This may be too late to help you, but I just ran across a card from a Budapest restaurant I've enjoyed a couple of times.

It's called Árnyas ("arnyash") and is located in Buda, near the János Kórház bus/tram stop. Street address is Diósarok 16. This is a residential district, but from what I can make out from the card, the restaurant has been in the same location for a long time - since 1906.

Food is good, so is the service. In warm weather you can sit outdoors on a sheltered patio, and neatly folded blankets on a bench near the door are available if it gets chilly.

Julie in Seattle