There are two different, separate systems in Tokyo.
The trains, and the subway.
You can buy one two or three day discount passes for the subway. Here is a link that I used to figure out how they work:
subway ticket pass
There is no senior discount that I can see.
BUT: they don't work on the train system. And the train system includes the Yamanote Line, which is a train line that circles the city and is very convenient. Including from Shinjuku Station.
As far as I'm aware, there is no discount pass available for the train system.
So you have to decide if you're going to use the subway system enough to make the cost of the pass work, while keeping in mind that this will mean avoiding the train system, and it's convenience.
If you want to do the research, here is a link to a good site for figuring out what the cost of a trip using either system will be:
Hyperdia
Whatever you decide, it's an excellent site for planning routes.
If you decide the passes aren't worth it, you can buy either a Suica or Pasmo card (they're available everywhere) which basically acts as a wallet: you put yen onto it, and then use it on either the subway or train system and it deducts the trip cost. No discount.
Have a great trip, it's an amazing city.