A one day unlimited ticket that covers all JR trains in Tokyo and a few stations beyond the Yamanote loop in all directions costs Y730. It's usually not economic to add a week to a JR pass just for local Tokyo travel, especially since it doesn't include the subways.

Most of the non-Nozomi shinkansen SOUTH of Osaka don't have green cars, maybe that's what you read about. I do agree that in non-holiday periods, you generally don't need a green car ticket to get a seat on most any train you want and regular seats are certainly comfortable enough.