Shinjuku to Koufu is about an hour and a half. It's over two hours from Nagano, and requires a transfer in Matsumoto.
The rail line going out to Noda-jou station does not continue out to Nagano. I have no idea where it goes, but the short answer is: nowhere useful. So Noda will have to be reached via Nagoya.
Despite its enticing (and somewhat misleading) name, Noda-jou station is not actually located right at Noda Castle. It looks like it's going to be about a mile and a half walk. Shades of Azuchi much? I wonder if there will be misleading, disembodied Shingen heads to lead the way?
Shirofan says that it's only a 10 minute walk, so perhaps the map is misleading.
I'm not convinced that Nagashino Castle had anything to do with the the battle at Nagashino. Further research is demanded.
It looks like now we are not going to do Yonezawa or Yamagata -- or possibly will day trip it if we decide to go. We will have to go out there again some other time anyway. And this way we may have enough time to poke our noses in at Samegao Castle (*cough*wishfulthinking*cough*) or some of the other really cool things out that direction.