4 Hour layover at HND - plan on leaving the airport

I'm so glad this thread exists. I have a 4 hour layover at HND. It will be from 7:00am to 11:00am on a Saturday morning. I know it is somewhat tight, but I am planning on leaving the airport. Traveling with 2 kids aged 12 and 9 on this trip.

So far, I plan to get on the monorail and go somewhere interesting.

I wish I had more time, but 4 hours is what I have to work with, and I'm determined to have some kind of a "Japanese Experience" / Photo Op in this 4 hours. Has anyone here done this recently and have any strong recommendation or success story that they could share?