I've never played my Hinata off of a Nanami either, so this is great for both of us! Though all I really have in mind right now is generic fluffy things like playing video games together and, inspired by finding this picture on Tumblr last night, Hinata being exhausted from lack of sleep and accidentally falling asleep while hanging out with Nanami or Nanami catching Hinata sleeping in a weird place and he would just be really embarrassed about it when he wakes up since it's always been the other way around, haha.

Sadly that's all I can think of right now, but if you have any other ideas then I'd love to hear them!