In Stockholm you will have a variety of powerlifting clubs at your disposal. STK (aka Sundbybergs Tyngdlyftningsklubb / Sunbybergs weightliftingclub) would be my recommendation. Many of swedens finest powerlifters train at the place. It's big enough, with lots of weights, barbells, machines and lifters.
There is also SAK (Stockholms atletklubb / Stockholms athleteclub), a nice little place in the basement of an apartment complex, many weightlifters there though, few powerlifters. Only the most necessary things.
Lastly, you do have SATS in Stockholm, a fitness chain, however with the recent trend in sweden with fitness, SATS in Stockholm is actually housing a lot of good equipment and spacing. A few of our own wayward members lift there occasionally.
EDIT: All places are quite within the central area of Stockholm. I know that there are even more lifting clubs around the place, but I do not know their names in particular.