Cross the famous tree-lined avenue to Darnózseli. There, look for the restaurant Horgony Tanya and order a serving of traditional Hungarian fisherman's soup. It will be an experience you will never forget! I can personally vouch for it.
Sausage lovers should definitely visit Gasztrofil Manufaktúra in Püski. It is only about 4 km away, where you can taste and buy excellent sausages and salamis. The shop belongs to a meat-processing facility that uses meat from its own livestock.
Highly recommended!