Deserves its excellent reputation. You will need to take a cab to get here. Nancsi Neni ("Aunt Nancy's") is in a hilly tree-lined suburban neighborhood of Buda. There is a high fence around the restaurant and in the summer the place doubles in size as the garden is open. Everyone eats out there, as it's often too hot to eat indoors until much later at night. We went in the early evening as we had our three-year-old son along, and he LOVED it (we enjoyed it also). There is a climbing structure in one corner of the garden, and the locals bring their kids as well, so our son had others to occupy his attention.
Portions are large, and the food is Hungarian traditional - little salads of salted cucumbers, great things done with meat and onions or chickens and paprika, cherry soup if it's the right time, plus very decent and often reasonable wines.
Note: You will need to position yourself strategically to avoid cigarette smoke if it bothers you. This is Hungary, and a LOT of people smoke, especially around meal time, and in outdoor restaurants especially this is not considered rude or unusual.