First of all, if you are staying for a few days and want to get good value out of your trip, do buy the Gothenburg city card that gives heft discounts or even free admission to heaps of places.
Then onwards to what we think you shouldn't miss if you have a few days in Gothenburg:
A great indoor fish and seafood market where you can get the best possible seafood in Gothenburg. Buy some fresh shrimp and enjoy them along the water front or buy something more extensive and bring home to prepare. Even if you don't want to buy anything, it's well worth a visit.
Gothenburg’s botanical garden
The biggest one in Sweden, over 1500 species of orchids for example. A nice stroll through a warm summer day is lovely.
Haga old town
Old town of Gothenburg, cute little streets, funky shops and great cafés. Marvel at the old conserved building and soak in the atmosphere.
A night out on Avenyn
No where in Sweden can you find so many restaurants, bars and nightclubs on the same street.
Liseberg amusement park
A rather large amusement park that has got different sections for different ages up to adults. Yes the rides are really scary but you can also just hang out, eat cotton candy and enjoy the day.. In December they decorate the entire place with amazing lights and it's very very pretty, a must if you are lucky enough to be there at this time of year!