Törökméz is a cute restaurant perched on Rózsadomb, the steep hill on the Buda side of the Danube. They specialize in breakfast foods that are inspired from around the world: there's everthing from tasty huevos rancheros to acai bowl, avocado toast, Cuban sandwich, and English breakfast (all €7-9). If you'd prefer something more indigenous to the region, go for the snappy frankfurters (€5), or the bundáskenyér (€3), which is similar to a savory French toast. Local Hungarian wines are also available. Being on the Buda side, away from the tourist-heavy areas, Törökméz draws a mainly local crowd.
Once here, it's worth visiting climbing up to the scenic tomb of Gül Baba, located almost around the corner from Törökméz. Gül Baba was a Bektashi monk who died in 1541 during the city's Ottoman occupation, and today his tomb is the northernmost point of Islamic pilgrimage in the world. It's a scenic and tranquil area with sweeping views of Budapest.