official site for visitors to Bratislava  

WiFi (pronounced 'whiffy' in Slovak) access is now widespread in hotels and cafes in the city. The area around the Primatial Palace in the old town is a free public WiFi zone, provided by Bratislava City Council, where you can surf on the benches in fine weather. In poor weather you can normally get a signal from inside the Primacial Cafe, in the palace courtyard.