im currently here in Tokyo on an Exchange Program at Sophia University. Been here about 2 months. I'll be here till the end of july.
Like someone has said already, life in Japan will highly depend on where you live. It's hustle and bustle always here in Tokyo, but if you get to live in smaller rural city life will be much different..more slow paced.
The thing about Tokyo is that there's WAY too many foreigners here especially at my school where it seems like it's the haven for American Exchange students. If you really want to learn Japanese, hope you get to go to a place more like Nagoya, Sapporo, or even Fukuoka. You'll definitely get a better experience and learn soo much more. Not that you won't or can't learn anything here in Tokyo as well..but it's so much easier to get in the zone where you constantly hang out with other foreigners and not have to speak japanese compared with if you go to other parts of the country.
Back to original question...it all depends on where you are. If you're in Tokyo, you can easily see everything in this city within a week or 2 if you take your time. Also, from here buses as well as railways are really easy and cheap to just about anywhere in Japan. Only 4000 yen each way from here to Osaka/Kyoto on a bus though it takes 7 hours compared with 2.5 on the bullet train. Something to think about if you are an exchange student on a budget.
PM me if you want to know anymore. Maybe we might even be able to meet up or something if you are in the Tokyo Area.