I lived and worked in Göteborg for many years. It is a nice and friendly city and a wonderful spot to base yourself for cruising in the Skagerrak and Kattegat,
Whilst it is a good cruising base I would say it is not a good place for a liveaboard. There are several reasons for this, the primary one being that if you live in Sweden you must have a physical address, i.e. a street address. There are ways round this. Maybe you have a friend who will allow you to register yourself as living at his/her address?
Another issue with Göteborg is the fact that, unless you get out of the city and into the archipelago, the water is fresh or almost fresh and it can freeze hard. Maybe you have a suitable boat that can withstand that kind of punishment?
There are many marinas in the Göteborg area and one guest harbour right in the centre of town. A friend of mine lived there on his ex. pilot boat whilst studying at the nautical college. Out of season the rates were quite reasonable but he had no services - showered at the college etc.
If you can be more specific regarding the area in which you would like to berth and live I could help you a bit more. Also, a little information about your boat would help.
I will be off-line until tomorrow afternoon or Friday morning due to a business trip in the far north of Sweden. More later then!