Document going shopping, for instance, or going to the beach. You’ll want to make sure that the most intelligent being in the known universe isn’t just telling you what you want to hear with its answers to, say, questions on a personality test. Actions speak louder than words.
Go out to a funny movie and see if it laughs at the right times. Get dinner someplace nice and make sure it doesn’t harass the waiters with rude or socially awkward comments.
If it has a mind to colonize a distant planet, don’t feel shy about volunteering to come along for the ride. Space travel may be an excellent opportunity for you to take notes on the AI’s relationship to the universe as a whole. Does it seem to harbor the same fundamental feeling of insignificance that you do?
Other enjoyable activities for you to do together may include founding international and/or interplanetary business ventures, staying in some nights and baking delicious pastries, playing golf, going to rock and roll concerts, starting a podcast, putting an end to cancer and other health concerns once and for all, and expanding your social circle by going on double dates.
If you come to the end of a long day together and you’ve filled up another notebook, it’s okay if you fail to record all the details about what happens after you turn out the lights—unless there’s not much to tell, in which case that might be an interesting detail to include.