Depending on the timing, you could catch the cherry blossoms blooming.

When we traveled to Tokyo last year, we did a 1-day Mt Fuji bus tour very similar to this one:



Meiji shrine and Sensoji temple are cool cultural and tourist attractions, but I recommend going very early (before 7am) if you want to beat the crowds.

We did both Shibuya Sky and Tokyo Skytree (on different days) to see a panoramic view of the entire city.

Ginza is a fun area for upscale shopping and good restaurants.

I haven't been to Kyoto or Hiroshima yet, unfortunately. We were in Tokyo for ~10 days and just scratched the surface.