Two days into our trip to Budapest, and we still had not found a restaurant serving authentic Hungarian cuisine that was not overtly pitched at tourists. Huszar was exactly the place we had been looking for when we eventually found it. The hosts were very friendly and keen to impress, the food was brilliant, and the place was full of locals.
We both tried a paprika and sour cream stew (one vegetarian, one not), served with Hungarian dumplings. These were not the stodgy, potato or bread based accompaniments you would expect, but more akin to a fluffy pasta. Absolutely delicious, and generously portioned too. The house white went down well with the stew, followed by a warming strudel.
Huszar is therefore highly recommended. There are English translations on the menus, as well as a range of vegetarian dishes.