I want to run a game or two before War of the Crown starts formally for my players to get used to the social system. Does anyone have and suggestions of any smaller adventures that I might use for ideas?
There are actually three Pathfinder Society Scenarios made entirely to set the stage for the War for the Crown AP:
Birthright Betrayed
The Jarlsblood Witch Saga
The Lion's Justice
These are all assumed to take place with separate PCs that aren't in the AP proper, though if you wanted to use the same characters Birthright Betrayed could potentially work as an introduction. Birthright Betrayed and The Jarlsblood Witch Saga both have notable social interaction segments you can apply WftC's social system to.
If you wanted to go a little crazier with it and foreshadow the villains of the AP a bit more, I did a fairly heavy revision which also tosses in three other scenario books. It would take a fair bit more prep to set this up though, so I wouldn't recommend it if all you're looking for is a quick warm-up, but I did include notes in my post about where you can insert social combat and social system rules in each of the scenarios.
Another idea if you're looking for an alternative is to pick something out of Honor's Echo and reflavour it as Martella testing the PCs. I haven't run these myself so I can't speak to how well you could adapt it to include the social system, but there might be some ideas in there.
I ended up making up my own little stories, which had some PCs as agents and others discovered across events. One group at a Wedding and one at a Hunt.