Tokyo Transportation

Hi everyone, I am having a lot of trouble understanding the japanese transportation system.

I am planning to stay in Tokyo for 10 days and will mainly be traveling to places on the JR Yamanote line. Should I purchase a JR East pass (which is quite expensive at about 25,000 yen), or should I just pay for the daily subway costs as I travel?

If you stay just in central Tokyo, you are typically spending about 500 to 1500 Yen per day on urban transportation:
http://www.japan-guide.com/e/e2017.html

A JR East Pass only makes sense if you travel large distances, as explained here:
http://www.japan-guide.com/e/e2361_02.html

Thanks Uji. Would you recommend purchasing a prepaid card - Suica or Pasmo?

I would recommend getting a Suica or Pasmo. If you are arriving from Narita Airport, there's a special package called SUICA & NEX, where you can get a narita express ticket to Tokyo and a Suica card with 1500yen loaded, a very good deal.

You also find the Suica cards to be useful not only with train tickets, but you can use them to make other purchases at stores for food and other merchandise.

If you are staying for two days or more and plan to use trains and subways frequently, I also recommend to use Suica or Pasmo. The details are here:
http://www.japan-guide.com/e/e2359_002.html