We recenly stayed in Budapest for four days and came to the Borkonyha twice. It was our favourite restaurant. The food and service was first class, with an excellent choice of traditional Hungarian dishes with a modern twist. Our waiter was most knowlegable about Hungarian wines and recommended two first-class selections.
You can eat outside (great for dinner) or inside, in air-conditioned bliss (great for lunch).
Great value for money as well (especially when compared to Dublin restaurant prices).
I highly recommend it.