Nagoya to Tokyo then Nagoya to Kyoto

Hello! I am planning on living in Japan and studying abroad in Nagoya. I want to see a lot of Japan while I am there and I am confused as to what passes I get. I want to go to Tokyo and know a day trip is not possible. So I would like to visit maybe for a few weekends and return to Nagoya in night or stay over in Tokyo. While in Tokyo, I also may travel to different parts of the city. Now I also want to go to Kyoto and plan on doing the same thing as Tokyo. Not to mention I will be needed a pass in Nagoya. Please help! Which pass or passes do I get,

Inside Nagoya, you can likely get a commuting ticket "teiki" (1, 3 or 6 month), which will give unlimited travel between two pre-specified stations on the subway/train/bus that you use daily. Possibly even a student version "tsugaki teiki", if you qualify for one.

For travel to Tokyo and Kyoto, if you are limited by time and want to take shinkansen, regular tickets are probably the best option.

Another option is overnight-buses, which could save day-time and money on getting a hotel in Tokyo. Kyoto is not that far, so a morning bus or normal train could work, if you want to spend extra 3 hours and save 7000yen.
http://www.japan-guide.com/e/e2366.html
http://willerexpress.com/en/
Willer bus pass may save a few yen for you:
http://www.japan-guide.com/e/e2369.html

If you are in Japan during "Seishun 18 Kippu" period, it can be a good deal: http://www.japan-guide.com/e/e2362.html