Will I need a JRail Pass for my trip to Japan

Hello, this summer I'll be visiting Japan.
I'll be there from August 14 till September 5.
I'll mainly be in Tokyo during my trip,
I have plans to visit Nagano for a few days (Girlfriends home town)

Will I need a JRail pass to travel around Tokyo?
If I don't have plans to leave Tokyo other than my visit to Nagano, is a JRail Pass worth it?
Should I get a week pass just for the one trip?
Or should I get one for the whole trip just in case an unexpected plan brings me somewhere else?
I should add I'm on a budget, and since they're expensive I don't know if they're worth it or not.

If you're going to get a pass, I would recommend this one:
http://www.jreast.co.jp/e/eastpass_n/index.html

It's 18,000 yen for a flexible 5 day pass. Since it is 16,400 round trip from Tokyo to Nagano that leaves you with only needing to spend 1600 yen to break even. Since the pass is flexible, you can use it to take the NEX from Narita to Tokyo, 1 day
Tokyo to Nagano 1 day
Nagano to Tokyo 1 day
NEX Tokyo to Narita 1 day

and still have 5th day to use it anywhere it is valid.

I would not get a standard JR Pass. It's 29,110 and is 7 consecutive days while the JR East is flexible.