Cafe Schwalbennest
A tiny old house turned coffee shop in the center of the city, Cafe Schwalbennest serves traditional Austrian cakes such as homemade sweet poppy seed and cheese-curd tort. It's also a great breakfast spot with regionally sourced cheese and meat, and has a nice Austrian wine list for later in the day. Green shutters on a red facade make Cafe Schwalbennest easy to spot, and there is an upstairs patio overlooking the River Mur, which runs through Graz. But beware, with only three tables upstairs, it can be difficult to snag a spot.