JR Pass if Tokyo only?

Hi Maia!

As you're staying in and around Tokyo and also arriving at Haneda, I think your best bet will be to simply purchase metro and local JR line tickets as needed. Looking at your itinerary you're unlikely to get good value for money from a Japan Rail Pass. You can read more here about prepaid travel cards in Tokyo.

For your Fuji trip be sure to buy a 2 day Hakone Free Pass, which will cover all trave from and to Tokyo up to the Hakone area.

Hope this helps!

If you're traveling all over Tokyo for several days, you might save money with a 3 day subway pass. The full JR Pass would be a horrible waste of money for just Tokyo.
You could spend a lot of time in Tokyo and still not see everything.
In Tokyo a few of the best places to see are the Tsukiji Fish Market, plus the site that every last tourist goes to see, the Sensoji Temple. If you are in Tokyo on a Sunday afternoon, be sure to go visit Harajuku to see the youth with their wild fashions. Meiji Shrine and Yoyogi Park are next to it and well worth seeing also. And be sure not to miss the Shibuya Hachiko intersection especially on a weekend when it looks like half the city is crossing the street at once.