"Roam like at home" - If you are a visitor from another EU country you will be charged the same amout as you would be in your home country. Different rules apply to non EU citizens. You may want to contact your local operator for local prices during your stay.
Landvetter Airport - Free WiFi is available at the whole airport for 3 hours or a maximum of 100MB data.
Central Station - Free WiFi is available both in main building and in the older part of the station.
Gothenburg Tourist Center - Free WiFi, ask the staff for password.
Many cafés and restaurants around the city also offer wifi hotsports. The cafés Condeco, Da Matteo, Espresso House and Le Pain Francais are all safe bets for a good internet connection. There’re some good apps and websites like Wifi Café Spots, WiFi Map for iOS and Wifi Finder for Android that helps you locate more hotsports around Gothenburg.