How about we… pretend we're tourists in our own city and go see the sights we've been meaning to...but haven't yet.
How about we… lurk at a coffee shop and make up stories about the couples who we think are there on a first date.
How about we… write down a bunch of random questions, put them in a hat and get to know each other by pulling them out, one at a time.
The movie I've watched the most times:
The Last Samurai