Just be aware that the City Hall only can be visited independently (from organised tour groups)
by going to the city hall and book you onto on of the official guided tours they have. So once
your into Stockholm you have to get there to book a tour. With that I mind it might be easier
to skip the City Hall?
In your case I'd say the shuttle bus would the #1 option, commuter train #2 and HoHo #3.
1. Shuttle bus :
Before you leave the port, buy a 24 hour travelcard . It will make things easier. https://www.google.com/maps/dir/59.3295875,18.0688823/Nordiska+Museet%2FVasamuseetfirstname.lastname@example.org,18.0737417,16z/data=!4m13!4m12!1m0!1m5!1m1!1s0x465f9d5370990379:0x2c9c68631fe28fcd!2m2!1d18.0954904!2d59.329367!2m3!6e0!7e2!8j1553500800!3e3
Walk 400-500m through Kungsträdgården to the top of the park and go with tram 7 to Nordiska museet.
Short walk from there to Vasa.
harbour ferry from the end point.
make your way through Old town to the Royal Palace. The shuttle bus pick up point is just
north of the Royal Palace.
1. Train (walk or shuttle from ship) Before you leave the port, buy a 24 hour travelcard . It will make things easier.
From Stockholm central station to Vasa.. You will arrive at Stockholm City station but exit via Central station
since City station is deep under ground. https://www.google.com/maps/dir/Stockholms+Centralstation/Nordiska+Museet%2FVasamuseetemail@example.com,18.0685061,15.25z/am=t/data=!4m18!4m17!1m5!1m1!1s0x465f9d60f602f26d:0x97c553dab672ba3d!2m2!1d18.0579323!2d59.3306685!1m5!1m1!1s0x465f9d5370990379:0x2c9c68631fe28fcd!2m2!1d18.0954904!2d59.329367!2m3!6e0!7e2!8j1553500800!3e3
Then the same was Shuttle bus except you have to walk back to the railway station
or use bus #2 this route: https://www.google.com/maps/dir/Slottskajen,+111+30+Stockholm/Centralenfirstname.lastname@example.org,18.0646941,16.75z/data=!4m19!4m18!1m10!1m1!1s0x465f9d58f0d51c9b:0xeed79a89224f260a!2m2!1d18.0724605!2d59.3279393!3m4!1m2!1d18.0636932!2d59.3276775!3s0x465f9d5f7ad5ac8b:0xa991e73560a93731!1m5!1m1!1s0x465f9d5fd41ea9a3:0x947f8c30d0eb3289!2m2!1d18.0599987!2d59.3301213!3e2
3. HoHo buses seems to be a bit unreliable according to some (doesn't leave until bus is full) posters.
It doesn't go between the things you want to see in a linear order but a detour around town as well
as up to Frihamen in a worst case scenario. You could combine it with the HoHo boats though.