Sweden is overall fine, we're generally depresingly car-friendly but you're never really car-dependent as such, even in the most turbo-rural areas you'll have access to a service that is basically taxis operated by the provincial public transport org and runs on the same tickets (though you won't want to rely on this), and in urban areas you can generally get around perfectly fine with both bike and walking (although walking will take a looooong time).

Stockholm obviously has the very competent subway (which is currently being extended by quite a lot!) and has a bunch of other local railways and an extensive bus system. Gothenburg has the largest tram network in the nordics and is refreshingly human-centric and it's only getting better.
Malmö is eeeeeeeeeh, it's got a weird quasi-subway with the commuter trains running through it to the rest of the region, but otherwise refuses to stop trying to solve all their problems with buses.

One interesting thing in sweden is that basically any vaguely sizable town will have one or several "suburbs" that are basically a bunch of commie blocks and amenities organized into a tiny town of its own, which will have reliable public transport connection to the public transport hub. This means that you can almost always find some vaguely affordable housing where you can live without ever needing a car.