It follows the eponymous Hana Uzaki who is at first delighted to be at the same college as her classmate from high school Shinichi Sakurai. But when she sees that he has a rather mundane lifestyle, she decides to take it upon herself to hang out with him.
I get that there was some slight controversy of the series because of some moral guardians being critical of Uzaki's design. If not for her...assets, she would easily be confused for maybe a high school or elementary school kid. Her being short not helping matters. But...the show establishes that she is a young adult as in reaching her 20s at best.
Pushing the controversy aside, thus far the characters are very enjoyable. There's Uzaki herself for starters. She is energetic and preppy as well as a Grade A troll who loves to mess around with Shinichi. She has the potential to be annoying, but she squarely falls under the "not too obnoxious" side for me partially because it is a more funny kind of annoying wherein the character or characters are the ones being irritated by her antics.
But she also has her good side. There are moments where she does unwittingly drive Shinichi off the deep end and she apologizes. Ultimately she does have a good heart where she wants to ensure that Shinichi does live fully.
Shinichi is a good foil. He tends to want to be by himself and enjoy that time and when Uzaki intervenes, you can understand his frustration with her. But he does find himself slowly enjoying being around Uzaki. Despite this, he does have a softer side such as loving cats and dogs. It's unfortunate that because of the perpetual scowl on his face, he comes off as imposing.
Supporting characters include Ami, her father, and Shinichi's only friend. Ami works for her father at his cafe where Shinichi works largely because of how attractive he is. This comes across as interesting in terms of Ami: she lusts after Shinichi because of his physique, but much like her father, she is a passive watcher of Uzaki and Shinichi taking an interest in seeing their relationship bloom.
Sakaki is Shinichi's friend who is a ladies' man who also takes an interest in the relationship because he wants Shinich to get a girlfriend which puts him in conflict with Ami due to him wanting to take an active approach in getting them together. He's kind of sleazy to me, but that's from a minor glance. He may get better over the course of the series.