This might be a fine hook for a story by itself but this wouldn't be much of a superhero comic if there weren't a little action to round out the drama. The date becomes even more awkward when a hired-gun in a nano-tech suit shows up wanting to fight. As will happen when you're Supergirl trying to relax. The action here is well laid out by artist Mahmud Asrar, who economically fits a lot of story into every page.
Michael Green and Mike Johnson have created a quiet classic with this series. Kara continues to impress as an intelligent, compassionate heroine. We also learn a lot about new cast member Tom here, seeing that he's bold enough to attack a super-being to protect a friend... even when the friend is a young woman who can break buildings with her pinky.
If you aren't already reading Supergirl, you should give it a shot.