There are lots of nice restaurants in Gothenburg.
At Olskrokstorget you have a nice tapas restaurant called Leonardo tapas and lounge, or a fantastic pizzaplace called Cyrano.

Some other suggestions is one of the Pinchos restaurants in the citycentre where you order small dishes via an app or phone. Great restaurant!
(in Swedish, but choose Meny and one of the restaurants in Göteborg)

Some links to restaurants:
http://www.goteborg.com/en/restauranger/
http://www.restaurangguiden.com/en

If you instead want to go for a traditional Swedish fika you should try Café Husaren on Haga Nygata 28, where they serve HUGE swedish cinnamon buns (on the photo)! A must!
To be shared…

Another very nice place is Bertilssons stuga which is a really nice place in the woods with open fireplace in the winter and also able to sit outdoors.
You will need a car or take a walk through the woods of Skatås to get there.
How to get there: http://bertilssonsstuga.se/wp/hitta-hit/
(not in Swedish but use Google translate)