If you have the JR Pass just book the cheaper Mt Fuji＆Hakone, and then take the bullet train at no extra cost on your way back. To be honest, we were pressed for time, and we would not have been able to fit so many places in one day on our own, so booking the tour was a must in our case.
However, prepare to be disappointed - we took a bus, a boat and a cable car to climb a mountain to be able to see Mt Fuji, but the climate conditions were so bad that we could barely see each other in the mist! And the timing is so tight that we only had 20 minutes up there anyway.
However, we did get a good look at Mt Fuji from a restaurant where we stopped for lunch. So although you might see the lunch stop as unnecessary, it might be the only opportunity to get a good photo of Mt Fuji.
The tour guide was informative, however, she was rude to people of colour to an extent that I, who was treated nicely, felt uncomfortable and could not wait to get off the bus.
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