I don't know what is your requirement for a "nice onsen", but I heard one of the few onsen in Hakone where we can see Fuji-yama as the scenery while we bath is Hotel Green Plaza Hakone. It is, surprisingly, not a ryokan, and I heard it was quite easy to access and are quite near the city (not so much "in nature").
I went to Yunessun, just for the bath. I found a super cheap place to stay nearby. It's quite big and there is two main sections, a "real" onsen one (you know, naked with the hot bath) and a bathsuit section with special bath (like wine an coffee). So it might be a bit more for fun with friends than just relaxing before bedtime. Not bad, bud if I had to go to Hakone again, I would go to a smaller place, something that does not feel like an atraction.