The story was pretty good.
Characters generally have motivations that made sense and didn't conflict with what they were doing in the story. I liked most of the characters a lot.
My main problem with some characters were how they were portrayed as not being monsters like the one love interest who is a serial killer. The character became a serial killer for extremely selfish reasons and yet the manga depicts the character as being more just a regular bad boy love interest. While there is plenty of vampire on vampire murder, killing humans is a crime in the setting and they don't need to murder to feed themselves.
Vampire rules sometimes feel like they are introduced purely for convenience and not in a way that feels very natural. The protagonist and the main viewpoint character doesn't understand the vampire world well, so it is not a huge issue.
I loved the art. The characters are drawn in a very old fashioned style that has fallen out of favor over the years. I love that style, but I understand a lot of people probably find it off compared to most more modern art styles.
I got a ton of enjoyment out of My Boyfriend Is a Vampire. I never felt bored while reading it all in one day, which is a rarity for me.