I've finished my first mission in Elder Scrolls: Betrayal of the Second Era and I've also procrastinated on making the turn sheet for it (see Activity Idea #2) BUT it's definitely a good idea because it would have come very much in handy.
For this activity idea, it'd be nice for it to be something music related. What about doing a "call and response" thing with Clara? We take it in turns to play an improvised melody, and then the other person copies it and does a varient on the same melody, and repeat. The melody gradually changes but at each step it's easy to do.
In a more advanced version one person leads with a very simple slow sequence of notes and repeats them while the other person riffs on top of it, eventually landing on a melody. Then we swap, I learn the melody and Clara plays the harmony. Once I've gotten the melody Clara modifies the harmony, then I modify the melody and we swap again, etc.