Arriving in Tokyo Early. What can I do?

So I'm going to Akita International University on June 22nd and I'm planning to depart on June 16th and arrive June 17th. What can I do in Tokyo in that time period by myself? My budget is probably $500. Tips on hotels, transportations, and life in general would really be helpful. What are some must see places in Tokyo?

Also, what is the best Method to get to Akita Airport on June 22nd. Thank You.

about Tokyo: you should have bought already a good guidebook!!! read A-Z at the very top of this forum for a start..
To go anywhere by train check www.hyperdia.com

Considering that you want to stay for five night in/around Tokyo before you get to Akita on 22nd, and that you have for the whole five/six days only $500 to spend, you should plan well and reseve hostels or reasonably-priced business hotel in advance.

As already suggested, check out the A- Z or Travel sections of this website for information on where to go in/around Tokyo :)

To get to Akita International University, according to the university's website:
- You could fly from Haneda Airport in central Tokyo to Akita airport (1 hour and 5 minute flight; 7 flights a day), then take a taxi (about 5 minutes),
OR,
- You can take trains. Tokyo - (4 hours on Akita Shinkansen "Komachi") - JR Akita station - (15 minutes on JR local line) - JR Wada station - (15 minutes on bus) - AIU.

Here are some suggestions I typed earlier about Tokyo:

I'd skip the Sony Building (been there, and was overrated to me, not much to do, practically just like going into a big Sony store.) If you're in to technology I'd check out Akihabara district. Also, if you're in to cars you can go inside all the cars at Toyota's multistory Amlux building in Ikebukuro. As for Tokyo tower, I did not go up in it, only near it. For another good view of the city, I'd recommend the Tokyo Metropolitan Government building in Shinjuku. (Check out the world's busiest train station in Shinjuku also). And Shinjuku park is near there too. The area around the Imperial Palace is nice to walk around, and the garden there and area near Yasukuni shrine and the war museum there are nice too. A unique view of the city that I'd recommend would be to go to Hama Rikyu garden which is along the water and has a good view of Rainbow Bridge. (before you go to the garden, check out Tsukiji fish market in the early morning, it's within 10 min. walking distance) Inside the garden you can board a boat to take the Sumida River cruise up to Asakusa. The cruise gives you a unique view of part of the city. In Asakusa you can go to Sensoji temple and then walk over to Ueno park and visit a museum or two there if you want. There are also some pedestrian walkways with shops and street vendors outside of Ueno train station. For night life I'd recommend Shibuya and the many busy pedestrian walkways/streets there. There's also Shinjuku and Roppongi for nightlife.
Check out the Tokyo Museum Guide also:
http://www.japan-guide.com/e/e3054.html

Also, you could take a day trip to Yokohama or outside of Tokyo into a more natural area. I'd recommend buying these books to bring along: Lonely Planet Japan, Tokyo City Atlas: A Bilingual Guide (3rd Ed.) (a must have), Streetwise Tokyo laminated map (very handy), Day walks near Tokyo, and Time Out Guide to Tokyo (a must have, in my opinion the best Tokyo Travel Guide book).

As for a hotel, I'd stay somewhere along the Yamanote line. Does not really matter where that much, b/c it only takes about a half hour by train to get any where on the Yamanote line (since it's a loop). Also, all the places I recommended are in good walking distance from the Yamanote line. Personally, I'd try to stay closer to Shinjuku and Shibuya side of the Yamanote line. But if you stay on the Tokyo/Ueno side there are a lot of things near there too.

I decided to buy the Times Out guidebook 5th edition and the Atlas.