Bratislava's old town is packed with restaurants, ranging from traditional Slovak food (bryndzové halušky — potato dumplings with sheep cheese — is the national dish) to international options. Prices are lower than in nearby Vienna, especially if you step a block or two off the Main Square.
For traditional Slovak cuisine, Modrá Hviezda below the castle hill is the best option in terms of quality and atmosphere. Slovak Pub on Obchodná is reliably filling and cheap. The Old Market Hall on Nám. SNP runs a Saturday farmer's market and occasional street food nights.
Govinda near the old town is the go-to for cheap vegetarian food. Zylinder on the Main Square has good terrace seating and a reliable kitchen. Lemon Tree covers Thai and international dishes competently. The Bratislava Civic Brewery serves hearty pub food alongside its own beer.