Should be do-able to get on the ‘Rainbow’ bus to the city centre – takes about 1 hr, leaves every 1/2 IIRC, cost about £20. Alternatively – take the speeder train – expensive though! Stockholm is probably not all that great shakes for a short while though, there’s not much to actually ‘see’ – what would you have – 1 1/2 hours, maybe?
Alternatively… you can do what I have done, which is walk straight out of the airport, across the carpar area, take a left at the first petrol station and keeeeeepp waaaaalking…
Eventually you’ll find a nice lake, with some scots pine trees and heather. I laid down in the sun there for about 8 hours in May, it was quite nice.
Probably not so nice this time of year though!