I'm an alumni !
I am an alumni of Waseda Univ. I graduated way back in the '90s - and am therefore much older than you- but I've enjoyed every moment of my four years of undergrad years and my two years in graduate school. In fact, that's where I met my husband!
You should know that Waseda is one of the best schools in Japan. In fact, it wouldn't be an exaggeration to say that it is the best private University in Japan, along with Keio University, so congradulations for being accepted as an exchange student! You should be very proud of yourself:clap2:
Unfortunately, I am currently living in Yokkaichi, Mie - much closer to Kyoto and Osaka than central Tokyo, so I wouldn't be able to help you very much in terms of places to go and things to do around the Tokyo metropolitan area, but I can assure you, there are plenty to see and plenty to do.
I've only been to Paris once for a week or so, and that was way back in the 90's when my parents lived in London, but Tokyo is much like Paris or London in the sense that public transportation is excellent - you can go Anywhere by train, subway and bus - and that you can find almost everything you need, whether it is food, clothing, books, clubs, etc.
So, enjoy your stay, but stay out of trouble - young foreign students are just as easy targets of crime in Tokyo as would be in any other big city. I hope your 2 years in Japan will be worthwhile.
Keep in touch!