I can't think of anything immediately interesting along the Sendai-Tokyo route that wouldn't involve taking another train. For example, you could get off at Utsunomiya and take the Nikko Line to...Nikko, of course. Or you could get off at Kôriyama and see Aizu-Wakamatsu, but again, that's a significant diversion.
If you want to see Mount Fuji along the Tokyo-Nagoya stretch, you're pretty much out of luck in the summer. As I have mentioned many times on this board, I was once within 10 miles of Fuji and couldn't see it, due to the haze. You are most likely to see it in the winter, when the air is dry. Forget the area around Shin-Fuji station. It's as ugly a stretch of strip mall sprawl as you are likely to find anywhere in Japan.
However, you might want to stop off in Odawara, which is the gateway to Hakone but also has a castle.
There's another castle in Hikone on Lake Biwa between Nagoya and Osaka. Change to the slow train at Maibara.
Or, take the Kansai Main Line all the way from Nagoya, stop off for the ninja museum at Iga-Ueno, the entire city of Nara, and the world's oldest wooden buildings, the temple at Hôryûji.
And of course, if you stop off in Kyoto, you're within walking distance of a couple of temples.