I haven't been on the E6 yet, but note that it will only go really fast (300 km/h+) on the Tohoku section of track, not the bit from Morioka to Akita. If you want a weekend trip that's scenic you could try catching a Shinkansen up to Shin-Aomori, then the very pretty Gonosen line around the coast to Akita and return to Tokyo on the Akita Shinkansen (E6). Hirosaki is a pleasant place to stopover with lots of apple treats and an interesting neputa museum. At Akita you can get some kiritanpo nabe from restaurants on the top floor of the shopping centre attached to the station.
An alternative could be catching the Yamagata Shinkansen to Shinjo, which is another pretty ride, a local train to Kakunodate and then Shinkansen onwards to Akita or back to Morioka and Tokyo. Or there are dozens of variations depending on which scenic local line you like to take! Just note that the Joetsu Shinkansen from Niigata isn't very scenic.
Sit on the left side of the Tohoku Shinkansens going north.
You can take a look at my blogs here
for more details and links to photos.
Apart from the area around Mt Fuji, I find the Tokaido Shinkansen line to be pretty poor scenically, though the trains are very comfortable. If you want a pretty journey, take local trains through the mountains or along the coast - some of the scenery is simply magnificent and often the trains are quite comfortable, if not always fast. See my travel blog
for plenty of examples. The only Shinkansen lines I haven't caught are all the way between Morioka and Akita, except for a short stretch Omagari to Kakunodate, the Nagano line between Nagano and Takasaki, and the Hakodate to Shin-Yatsuhiro stretch of the Kyushu line to Kagoshima (still under construction at the time)