If you feel that downtown’s pastry shops offer a slightly touristy experience and prefer to go someplace that locals also frequent, head to Nándori Cukrászda. This popular neighborhood joint, which is reachable from downtown by foot, has been going strong since 1957. You'll find here classic Hungarian cakes, tarts, savory biscuits, marzipan figurines, and also ice cream in the warmer months. They're remarkably consistent and just a notch below those of Budapest's celebrated hot spots like Gerbeaud and Auguszt.
Most recently, I’ve had an excellent Rákóczi túrós here, and an unexpected find was the light and tasty képviselő fánk, a profiterole-like cream puff with vanilla custard and whipped cream. On Saturdays, it’s not unusual that a line stretches outside the premises. Almost across the street from here is Jedermann Café, a local’s favorite bar that’s also worth a visit.