Modern Hungarian cuisine
21 - Hungarian Restaurant was the best restaurant I tried in Budapest and an excellent introduction to Hungarian cuisine. The restaurant, located just steps from the spectacular Matthias Church in the Castle District, serves up classic Hungarian fare with a modern twist and is popular among tourists and locals alike so make sure to reserve a table for lunch!.
When we went, they had a special menu for St. Martin's day (a local holiday) which revolved around goose, a revered ingredient in Hungarian cooking. We ordered goose foie gras over stewed apples and sweet potatoes, grilled goose breast over an apple-barley risotto with blueberry reduction, and an oven-roasted goose leg with stewed cabbage and grilled potato cakes. The foie gras literally melted in your mouth and the tart apples perfectly cut the fattiness of the foie gras. I had the goose leg which came with amazing, crisp skin and meat so tender it literally fell of the bone. As good as the goose was, my favorite part was actually the potato cakes. They were somewhere between latkes and hash browns, but were addictively good. As far as the food goes, you're going to be happy.
The also have an extensive wine list of Hungarian wines which can be difficult to navigate if you're not familiar with Hungarian varieties and regions, but we asked our server for her recommendation and she brought us a nice, crisp Gewürztraminer-style white wine with went great with the unctuous goose. They also had a small selection of Hungarian craft beers (I'd suggest the Tavoli Galaxis IPA, though it's a bit bitter to pair well with such delicate food).
The prices run from about 8-15 euros per plate on average, putting it slightly higher than the Budapest average but still more than reasonable for the quality of the food and the size of the portions. If you're looking or a good place to have your first meal in Budapest, I couldn't recommend 21 - Hungarian Restaurant more!