Yokohama resident and multiple-time Hakone traveler here.
If you're heading from Yokohama to Hakone by train, you'll go trough Odawara Station on the way. You can purchase a Hakone Freepass that you can use for trains between Odawara Station and Hakone Yumoto Station, as well as various types of transportation inside Hakone itself (busses, boats, ropeways).
The Hakone Freepass from Odawara costs 5,000 yen, which is cheaper than the one from Shinjuku (Tokyo) which costs 6,100 yen. Once you're in the town of Hakone, though, the passes are essentially identical (details here:
https://www.odakyu.jp/english/passes/hakone/). The Freepass can also get you discounts on certain museums and shops in Hakone, if memory serves.
If you're planning to do the full loop around Hakone, the Freepass usually ends up saving you some money. It's also convenient, especially if you're a first-time traveler or don't speak/read Japanese, because it eliminates the need to figure out fares and deal with ticket machines. Just show the pass and you're good.
As for must-sees, Owakudani and Lake Ashinoko are the top two, as they're both beautiful symbols of the city. Visiting a hot spring is also a must-do, but which one depends on personal preference, budget, and whether you're staying overnight or just going fr the day.
