I am also interested in info on Gothenburg, but as a two week holiday destination in July/August, ideally a few days in Gothenburg and the rest of time in campsite or other self catering somewhere within driving distance of the city.
Just back from Gothenburg and it is a beautiful city, very easy to get around and something to interest all the family. I got info from Swedish Tourist Board prior to going and there are many helpful websites. We got the Gothenburg Pass for 24 hrs which is worth it if even going to a couple of sights in the day and using public transport. I think it can be bought online before going as it can then be used on transport from airport. Just be aware that the 24 or 48 hr period commences from the time of first usage.
We had no probs with Ryanair flts to Save (Got City Apt) which has basic facilities but is only 15Km from city. Stayed at Lilotel outbound which I found on the airport website - very nice - maybe a little expensive but it was difficult to get accommodation the week we went. Last 2 nights stayed at Hotell Kusten which was so reasonable for family room I was expecting some basic hostel. It turned out to be a 1 bed + sittingroom and kitchenette that could sleep 6.
Haven't got the cc bills yet however eating out for family of 4 seemed to be not any more expensive than here if even.
We stayed in a hotel called Spar Majorna. It is along the estuary just passed the Danish Stena Line dock. We had a car while we were there which was handy but they seem to have a good tram system. The airport is about 15Km east of the city. The centre of Gothenburg has one of the biggest shopping areas in Sweden. We spent a good day wandering around the shopping area as it has a huge indoor and oudoor centre. You can take a walk down to the port where the 'lipstick' building is. It's the tallest building and the view from the top floor isn't bad. There is a tall ship in the port that is now a restaurant - didn't get to visit it unfortunately.