Visiting Hakone
Plan the transport carefully, don't pin everything on seeing Fuji, and try an onsen - the rules are simpler than they look.
Hakone is the slow part of a Japan trip. Three things made it work for me.
Plan your transport well
Hakone is not like Tokyo or Kyoto. It's more nature-focused, and transport can take time because you'll use a mix of trains, buses, cable cars, ropeways or boats depending on what you want to visit.
I'd recommend checking your route in advance and not planning too many things in one day. Hakone is best enjoyed slowly.
Check the weather before going
If you're going to Hakone hoping to see Mount Fuji, you need to know that the view really depends on the weather. Even if you're there, you might not see it if it's cloudy.
I'd still go because Hakone is beautiful, but I wouldn't plan the whole trip only around seeing Mount Fuji.
Try an onsen if you feel comfortable with it
Hakone is a great place to try an onsen. It can feel a bit intimidating at first because there are rules, and you usually need to go without a swimsuit.
The most important things are to wash before entering the bath, keep your towel out of the water, and stay calm and quiet. Once you understand the rules, it's actually a very relaxing experience.