Törökméz is a cute restaurant perched on the verdant Rose Hill in Buda, meaning that you'll need to cross the Danube to get to it from the Pest side. Törökméz specializes in breakfast food with on-trend dishes inspired from around the world: there's everthing from tasty huevos rancheros (€7) to acai bowl (€7), avocado toast (€7), Cuban sandwich (€5), and English breakfast (€8). 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. They also serve local Hungarian wines. Being on the Buda side, away from the tourist-heavy areas, Törökméz has a mainly local clientele.
Once here, it's worth visiting 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, and also a scenic and peaceful area with sweeping views of Budapest.