Been a while but I seem to remember that there were water taxis between the islands too, I took one to the Vasa museum island.
Found the underground good, you have to buy the tickets aboveground though,at a newsagents called a "Pressbyran" I think, loads of them around anyway.
Great and unusual confectionary if like me you're a fan of the sweet stuff.
There's a good tourist info office in the airport too, I think that we arranged a transfer direct to our hotel from there.
Enjoy your trip Foxylady!