It's interesting to see folks suggest Shinjuku-Matsumoto-Nagoya-Kyoto as an "alternative route" to taking the shinkansen directly to Kyoto. It's a great trip but it is hardly an alternative unless you've got a fair amount of extra time and also have a JR pass to avoid the substantial extra fare!

I've done it and with a 2-3 hour break in Matsumoto to see the castle and a few other less important sites, it meant starting early in the morning to reach Kyoto by evening. I think the Matsumoto - Nagoya part is the prettiest, but in any case, the limited expresses to and from Matsumoto are pretty slow because the tracks curve a lot.