Tokyo - Fuji/Hakone - Kyoto - Tokyo

Hello All. My husband and I are headed to Tokyo for the 3rd time and we have seen all of the places listed in my subject line but this time we are bringing a friend who has never been. We are only there for 9 days and we really want to do a 2 day trip outside of Tokyo and take him to Mt Fuji/Hakone and Kyoto. I figured we leave Tokyo in the AM, head to Fuji/Hakone by bus or shinkansen, spend the day, then hop the shinkansen headed for Kyoto, spend the night there, then tour Kyoto all day next day and head back to Tokyo from there. I have never done the trip like that before and I totally don't even know where to start. Any advice on how to go about this? Thank you in advance!!

Hakone is a resort area enjoyable in a single day visit. If visibility is very good, you can see Mount Fuji from there. But if you wish to go closer to the mountain, e.g. to the Fuji Five Lake area, then it will be difficult to cover both in a single day.

The rest of your itinerary is extremely fast paced (Kyoto has enough major sights to easily spend more than a week). It is like visiting New York for just 24 hours. But I have met people who like such a fast pace. If you do, then it can be enjoyable.