We stayed at the Hotel Reisen in Gamla Stan. ( now in the Hyatt family) Comfortable with a good breakfast. Walk to the Nobel Museum and the tour boats. gamla Stan is the best area to stay. Lots of good restaurants within an easy walk. The best tour for us was a trip to the Archipelago on the public ferry. ( Not the tour ferry). The HOHO bus was a disaster.
I would skip the train from the airport in favour of a taxi. The rate is fixed.