You can't see the sights of Hakone on a JR Pass.
But you can go to either Odawara Stn or Mishima Stn by JR, and then use a Hakone Free Pass to tour the area.
You didn't mention where you are coming from. But both JR stations have bullet train stops, so it can be convenient. There is a Hakone Free Pass that you can also use from Shinjuku.
The Loop Course is a common way to see all the sights and takes a full day.