Stockholm accommodation location advice

May I ask why you didn't consider Östermalm? It's equidistant to Gamla Stan and Djurgården, the two main sightseeing areas. You'll be better situated than with options B and C, both of which are out of the way.

No worries! All these options are central. Choose one of the two nice ones instead of Gamla Stan/Old town. B. Rådhuset is about as central as you can get and you can quickly walk to City Hall, Gamla Stan and the main train station. C. Odenplan is a bit more leafy and spacious, and within the city center, meaning, among other things, that the buildings are from the 1890-1920 period and that you can walk straight down Dalagatan or Upplandsgatan to reach the main train station in 15 minutes or less. Or travel 3 very closely spaced stops on the subway to get there. The Odenplan alternative is also a bit more authentic than the others, and if you like this flat best make a booking now. If you stay near Odenplan, or are in the vicinity, you should try the excellent gelato at Snö (snow) on Odengatan, just as good as, or better (!) than in Italy. The menu changes daily and there are many varieties. Black currant with licorice root was an unexpected flavour. I always order browned butter gelato with rosemary, which is a mainstay, and also pistacchio. Across the street there is the lovely Vasa Park with a recently renovated playground.

As long as you are close to a metro station you are in a good location, so really not that much to worry about. That being said, Gamla stan can be a bit crowded in the summer so maybe not the place to stay if want a calmer area, in which case Rådhuset is probably better. Kungsholmen is a mostly residential island and apart from the city hall the island sees fewer tourists than other parts of the city. Odenplan is not a bad location. Apart from being a metro station, the local trains also stop there and it is a major bus hub, so not that bad for getting around the city.

Thanks, everyone, for your input. I really appeciate it, especially how prompt it was!
In the end, we have decided to go with the Rådhuset option as that looks to work the best for us.
Thanks!

On a related note, Cherryplanter's Odenplan gelato recommendation definitely was intriguing.
Are there any special recs for the area near the Rådhuset metro station?