From my limited experience in Japan, the best views I have seen so far have been on the kintetsu line passing through Mie Prefecture from Yokkaichi through Iga and down to Nara Prefecture. There are some very quiet and tiny train stations there with rice fields and a backdrop of mountains on both sides. Very relaxing ride. I've heard that the views on the Romancecars to Hakone are also good, but personally have not tried it myself. Hope this helps!
I used my car much more frequently in Kyushu but the road up to Aso town in central Kumamoto parallels a part of the train line. On a clear day, the views of the five peaks of Mt Aso and the northern rim of the old caldera are just stunning. The train doesn't run that route too often, but if you're stuck waiting at the station, you have an amazing view!
The train line from Arashiyama to Kameoka is stunning vistas of mountain ravines, forests, and rivers. Either the standard JR line or the tourist trains give great views.
One of my favorites is the Sakuragi-cho Station on Negishi Line. I've been there more than 3 times just because I like the place. A tour around the station is more than enough to fill your itinerary for the day. But unlike the natural views than others recommended, it's more of a tourist attractions like a huge training ship, parks, a pond with colorful canoes, colorful ferris wheel, some shops and cool tourist buses.