Both Stockholm and Gothenburg are really nice cities - they're pretty safe too unless you seek out drug lords or park your bike without a decent lock. Just don't come here during the winter - you'll be depressed by the lack of daylight.
I don't think many tourists would head out to the far away suburbs by subway. My recommendation is to avoid Drottninggatan and "City" with the exception of some architecture or particular places of interest because it is just really too much busy people and pickpockets and hot asphalt and concrete and glass and tourist traps and chain stores.