If you don't mind splitting the onsen from the hotel, I highly recommend the private onsen suites at Hakone Yuryo (
http://www.hakoneyuryo.jp/english/hotsprings/), which I've visited a few times.
You didn't mention price - a nice, memorable Ryokan experience can easily top $800-1,000 per night.
Gora Kadan is a somewhat 'foreigner friendly' Ryokan option in Hakone with open air baths outside some of the rooms or suites, but can be pricey.
http://www.gorakadan.com/index_english.html?mode=pc