During their date, they could run into some of their old friends from the ninja academy. This would lead to some reminiscing and funny stories being shared. Or perhaps they encounter a small problem in the village that they work together to solve, which brings them even closer. Another possibility is that Naruto tries to impress Sakura with a new jutsu he has been working on.
Well, they might have a deep conversation. Naruto could open up about his dreams for the future of Konoha and Sakura could share her medical ninja goals. They might also get into a friendly sparring session as a form of entertainment during the date.