Navigating Fuji-Hakone-Ito

Hi! My family and I are visiting Tokyo this October. We would like to make a trip out to see the Mt Fuji, Hakone and Ito areas. What is the best way to do this?

- Is there one place we can stay as a good ''base'' for exploring these areas? we thought about Odawara, but there are so few hotels there.
- If we stay in one spot, say near Hakone-Yumoto, are there day tours that can take us to Mt Fuji, and around the Hakone area?
- If we stay one night in Fushiyoda, one night in Hakone-Yumoto, and one night in Ito, and traveling with the Fuji-Hakone pass and then the JR line to Ito, is it difficult to lug suitcases around with us while trying to navigate the public transport system from one place to another, and then back to Tokyo?

Thanks in advance for your advice!

It depends on where you mean by Mt Fuji. Mt Fuji can be viewed from lots of different places (e.g., Kawaguchiko, Yamanakako, south shores of Ashinoko (which is considered to be in Hakone area), etc.).

I'm hoping to explore lake Kawaguchiko, and perhaps take the Fuji Hiking bus to 5th station
And take the Mt Kachikachikyama Ropeway gondola to mountain observation deck and Lake Kawaguchi cruise.