What is the best way to get a feel for Hakone in 1 day travel from Shinjuku

Hi, I would recommend taking the Hakone Tozan Train to Gora after arriving at Hakone-Yumoto station from Shinjuku. After looking around,  take the Hakone Tozan cable car to Sounzan station so that you can  the Hakone Ropeway from there. Get off at Owakudani Valley to see the natural hot spring. Get on the ropeway again and get off at Togendai station. You can enjoy the view of Lake Ashi before getting on the Lake Ashi cruise to Hakone-machi. Lastly, take the Hakone Tozan bus back to Hakone-Yumoto station.

This webpage also gives you a similar idea for your itinerary. https://planetyze.com/en/japan/hakone/itinerary/hakone-golden-1

I hope you have a nice experience!