6D5N tokyo-kawaguchiko-hakone-kamakura-tokyo

Hi

My family of 4 will be travelling to Tokyo in Dec.
After staying one night in Shinjuku, we would like to go :
1) from Shinjuku to Kawaguchiko for 2 nights
2) from kawaguchiko to Hakone for 2 nights
3) from Hakone to Kamakura for 1 night
4) back to Shinjuku from Kamakura

However, I can't seem to find a suitable Odakyu pass that suits my itinerary. The closest is Hakone fuji pass that's valid for only three days.

Do you have any advice regarding the type of passes I should be getting? Thank you very much.

There are no pass that will cover all those days and include travel to and from Tokyo. You would just pay for travel between your locations, and then use local passes to cover the localized travels.

You would be better off reversing your itinerary and visiting Kamakura first. Then off you Hakone where you can purchase a 4500 yen Hakone Free Pass at Odawara for 3 days. Which will cover the buses half way to Gotemba at 16XX yen. Pay for bus Gotemba to Kawaguchiko. Buy the 2000 yen 2 day bus pass for Fuji 5 Lakes area. Then either bus or train back to Tokyo/Shinjuku.

Thanks!
I read somewhere that Hakone free pass can also be purchased at Gotemba?

No it cannot be purchased at Gotemba. Only at Odakyu Rialway stations. Which is why I suggested to reverse the itinerary.

Actually, the Fuji Hakone Pass is only 1150 more than the Hakone Free Pass. So it is probably better to get that as it covers the 16xx yen Gotemba to Kawaguchiko highway bus. And you'll have the buses within Fuji 5 Lake area covered for your arrival day.