City Hall is covered on the tour.
I highly recommend the Stockholm Pass 72 hours with transportation. If you watch the website there is a good chance you can purchase it on sale. It covers sites and transportation. It will allow you to pop into a few museums for a short spin without feeling that you have to get your money's worth at each stop. http://www.leisurepassgroup.com/
I absolutely loved Stockholm. If I could get my family to go and I could continue my career there, I would move!
If the tour is staying at the Wellington consider getting a room at the guesthouse. It is around the corner but less expensive. There is a nice lounge, breakfast room and kitchen. The hotel provides breakfast and dinner.
I would definitely spend one day on the archipelago.Take a full day cruise https://www.stromma.se/en/stockholm/sightseeing/
The tour goes to Gamla Stan, but I would spend at least another half day there.
I recommend walking on the raised path on Monteliusvagen. That is the vantage point of most of the photos taken of Stockholm that you see in the media.
I wasn't impressed with Skansen. But I live in Ohio and we have a bunch of parks like that. The Stockholm Pass does cover it. If I had to do over again I would have spent that time just walking around Djurgarden.
I loved this tour, if you have any questions about anything please ask here or private message me.