My sister and I spent a few days in Tokyo, then took a train to Hakone near Mt. Fuji, and ended our stay in Kyoto. We took a sushi-making class in Tokyo, stayed in a ryokan (traditional Japanese inn) with a hot spring bath in Hakone, and experienced a tea ceremony and explored shrines and gardens in Kyoto. Public transportation is excellent; I'd recommend the Japan Rail Pass (note you need to order it outside of Japan in enough time for them to snail mail you a voucher). I'd definitely visit again!