Hakone and Mt Fuji
Hakone is a vast area known for its hot springs, multiple modes of transport and views to Mt Fuji. Located between Tokyo and Kyoto it is a common place for visitors to spend a night at a traditional onsen ryokan (Japanese Inn). Hakone is also known for its mixed modes of transport as part of the Hakone Round Course, including bus, switchback train, ropeway, cable car, and even a Pirate Ship! The views across Lake Ashi allow some nice views of Mt Fuji in the distance on clear weather days. Hakone also has a number of other attractions including the Hakone Open-Air Museum.
There are a large range of ryokan in Hakone spread across the region. Note that most do not have views of Mt Fuji but many are nestled amongst the nice mountain/forest scenery, or in the smaller onsen towns. Ryokan like Aura Tachibana or Manatei are good examples, offering a traditional ryokan onsen experience. Most have Japanese style beds but there are a number that offer mixed western style bedding in Japanese style rooms.
Kyoto - It is approximately two hours from Kyoto to Hakone by Shinkansen.
Tokyo - approximately 90 minutes by train or by Shinkansen allows passengers to arrive in the main Hakone area.