Tokyo Rail Travel

We are looking to spend around 28 days traveling Japan and are looking into the easiest way to get from one area to another.. We are planning to spend a week in Tokyo itself before heading off to other locations using the 21 day JR pass.. Is there an alternate way to travel around Tokyo itself or is it best to just get a 7 day JR pass and then the 21 day pass to follow after..?

There are certainly cheaper alternatives to a 7-day rail pass for travel in Tokyo, unless you spend to plan spending more than 40 dollars per day on urban transportation:
http://www.japan-guide.com/e/e2017.html