Hi,
Since nobody else is around on the weekend, I will try and give you some info.
JR can take you to several popular places in Tokyo, but not all. I suggest you familiarize yourself with this map of the JR Yamanote Line
There are some places that you mention that are near a station and within walking distance, while others not so much. Sensoji and Nakamise are pretty much together, but not near any JR station (Ueno). The Sky Tree is even farther away. The Imperial Palace is not far from Tokyo Stn., and Kabukicho is next to Shinjuku. Meiji Jingu is very close to Harajuku Stn. Tsukiji is a bit of a walk but not too drastic, from Shimbashi. You could get to Yasukuni from Ichigaya Stn (Chuo Line) or see it after the Imperial Palace. You can get to Ginza from Yurakucho Stn. The Pokemon Ctr is not far from Ikebukuro. You can use JR from your hotel from Shin-Urayasu Stn to Tokyo Stn. on the Keiyo Line. I don't recall the rest of your itinerary, but this assumes you are making a JR Pass worth it by some long distance travel elsewhere - otherwise you are wasting an incredible amount of money on a JR Pass just within Tokyo. For more info, you also might see here
You might want to look at a 2 or 3 day subway pass if you want to get to some of these places the fastest.
Best of luck.
