Hakone Round Trip Course

I would like to buy the Hakone Free Pass and do the Round Trip Course at a more leisurely pace. Hence, I intend to spend a night halfway through the course. At which point can I find accomodation that is located at a convenient location for me to move on to the next stop in the morning?

I recommend Gora or Togendai. But it depends a little bit on what along the course you intend to see (and which direction you are traveling).

I'm following the route recommended by japan-guide i.e. going counter clockwise and stopping at the main attractions. I will enjoy the lake and the lake view. How much time does it take to cover the whole round trip in a comfortable (not mad rush) pace?

Then, I recommend a hotel or ryokan around Togendai/Kojiri.