Thank you all for your very helpful suggestions. You've convinced me to stay the night in Hakone at a traditional inn. (For what it's worth, my two nights in Kyoto will also be traditional style inns).

The reason I am taking the Romance Car vs. the JR pass train is that I've heard the view is beautiful from that particular car. I've booked a front-reserved seat. Maybe this was a waste of $10... oh well.

I feel much more confident in my decision now. Thanks again!