The Cute is everywhere in Tokyo, and you're not going to escape it. You shouldn't even try. This is a city with fluffy animals on every corner. Where buses prowl the streets disguised as pandas. Where every corporation and even the police force have their own charming mascot. The Cute cannot be avoided, so you might as well embrace it.
It's not the best place to take a date, nor would you want to visit after eating a large meal, but the Parasitological Museum in Meguro makes a wonderful excursion for when you... I mean, it's fun if you're in the mood for... Or, it's interesting for those who... You know what? I'm drawing a blank. I can't think of a single non-creepy reason to visit the Parasaitological Museum. Unless you're a professional parasitologist. (Even then, the very fact that you're a parasitologist is kind of creepy.)