If you’re touring Castle Hill, be sure to stop by this local favorite for lunch. Set in a landmark building that dates from the 13th century, Pierrot opened in 1982 as a coffeehouse (hence the name) but has since morphed into a fine restaurant. Banquette seating lines walls adorned by pierrot drawings, large mirrors and contemporary art. The menu offers an elegant mix of modern European and Hungarian dishes, such as grilled goose liver. Some bemoan that the restaurant has become too touristy, but it still draws both well-heeled locals and visitors, and the food is terrific. Open daily.

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I stumbled upon Gerlóczy Káveház by chance—in a desperate attempt to find an open restaurant around Váci Utca on a Sunday—and ended up returning twice in the course of my weeklong trip. Located on the ground floor of a residential building on leafy Kamermayer Square, the restaurant serves delicious Hungarian-French fare, including daily specials that are fresh and simply prepared. A recent lunch included goose pâté, and salmon en papillote with fresh lentils, washed down with a glass of Hungarian Champagne. Be sure to order some of the many varieties of breads; they’re baked fresh on the premises daily. After returning home, I learned that Gerlóczy was featured in the Steven Spielberg film Munich, so it’s not a totally undiscovered find, but I barely heard a word of English spoken here; instead, the place drew a mix of local families, couples and groups of friends. Open 7 A.M.–11 P.M.; Sat. and Sun. from 8 a.m. until 11 p.m.

Young, fun and inexpensive, Menza is right on buzzing Liszt Ferenc Tér and draws a 20- and 30-something clientele with its modern and traditional Hungarian fare. It has two levels (for a quieter dining experience, ask to be seated on the mezzanine) and a retro 1960s design with black-and-white floral wallpaper, high ceilings and cartoon-like gardenias decorating the tables. Skip international fare, like the mayonnaise-laden club sandwich, in favor of Austro-Hungarian specialties, like Wiener schnitzel, homemade goulash and stuffed cabbage (töltött káposzta). Open daily.