One day in Tokyo and one day in Fukuoka

I’m traveling to Japan on a very short study abroad trip where most of the days have a strict itinerary. The only time I can plan for myself is one day in Tokyo and one day in Fukuoka. I know there is a lot to see and I won’t get to see and experience it all, but I was wondering what people consider a “must see” for these two locations. I’m open to all suggestions!