Bagels rarely appear on Budapest breakfast menus, so I automatically order them when they do. Budapest Baristas, a small specialty café and breakfast restaurant in downtown, offers seven kinds (yes, the boiled-and-baked version, although they aren't made in-house). Apart from smoked salmon (€6), the other toppings are unconventional and include things like avocado cream and a combo of brie cheese and cranberry jam. They're perfectly fine, but keep in mind that Budapest isn't a bagel capital like Montreal or New York.
There's also other fashionable breakfast foods here like pancakes, granola, and eggs Benedict. Note that the portions are on the small side—most people can easily handle two plates. A La Marzocco machine is in charge of the espresso-based drinks that are supplemented by pricey matchas and filter coffee. Finally, a note of caution: Depending on who's behind the counter on a given day, service can be a little grouchy here.