JR Yamanote Line monthly pass

Hi!
Me and by boyfriend are planning to go in Tokyo for 2 months.
We'll be using the train everyday, I was wondering if there was a monthly pass for metro and how much it costs?

No such thing other than a commuter ticket for a month but that only works for two predetermined and specified stations. Get an IC card a top it up as you go.

As John B digs Japan says, if you are going to be commuting to a specific location (for example to a school) every day, or at least 4 times a week, you can get a commuter pass for that route. But there is no pass for zones covering different destinations. So it is recommended to get a prepaid IC card (either SUICA or PASMO around Tokyo area) and top it up, though this provides no discount.

By the way, "Metro" (subway) and "JR Yamanote" are different lines :)

A commuter pass between two stations can be any two stations; JR, subway and private railway.
My pass was from Hoya on the Seibu private railway to the JR Gotanda station passing through Shinjuku. I could get on and off at any station in between.
Tell me the exact stations you will be using and maybe I can figure out the best routing, etc.

Tell me the exact stations you will be using and maybe I can figure out the best routing, etc.

I believe that's what Hyperdia is for. ;)

We wanted to visit the most famous places in Tokyo, such as Shibuya Shinjuku Akihabara etc.
Which are all in the JR Yamanote line, that's why I thought maybe there was a monthly pass just for this line.

We're going to live near Hamamatsuchō
I saw that Hamamatsucho is pretty far from the zones we want to visit do you think we'll spend a lot for metro with a normal Suica?

A total offtopic question does anyone knows if thes renters are affidable?
http://www.modernguesthouseliving.com/en/
http://www.bamboo-house.com/index.php

Thank you very much for the help! :)

Unless you have lived here and used a commuter pass, (supplied by most companies) you can't know all the ins and outs aboutit.