Well I went and checked an old post I made at a swedish strenght forum when I was still living in gothenburg and looking for a good solid powerlifting gym...
There turned out to be two real hardcore gyms GSK and GKK both is powerlifting gyms... GSK is out at Stigcenter, GKK is at Slottskogsvallen, I know Stigcenter is located a bit outside the city, I am not 100% sure where Slottskogsvallen is but I think it is pretty close to central gothenburg, propably just a few tram stations out or something...
Now if your not allergic to commersial gyms there a quite a few in central gothenburg, and as I mentioned my favorite was a SATS high up on kungsgatan, I trained there myself a year or so and they got enough barbells and dumbells to be happy, definitively not a hardcore gym though, I payed around 400 swedish kronors a month there which is pretty standard in Sweden and not to bad for being Gothenburg...
Edit: and if anybody is interested in martial arts gyms in Gothenburg I can definitively point you in the right direction depending on what your interested in...