Nagano is certainly the best bet if you want to try the Shinkansen but I would not rule out Hokkaido. Domestic flights are not as expensive as they used to be (and the Shinkansen is not cheap.) A new regional airline called AirDo (for Hokkaido Airways) has regular flights from Tokyo-Haneda to Sapporo for not much more than a bullet train ticket. Worth checking out.
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