-as others have said, if you're not traveling outside Tokyo immediately, you should wait to activate your JR Pass until the first day you make an inter-city trip. Activation can be done at the 'midori no madoguchi' (reservations office) in any major JR station - I usually get mine done up at Ueno or Tokyo the following morning after arrival. In-town JRP is useful but not saving much - crosstown trips are generally 160-320 ‰~ within Tokyo or Osaka anyways, but a one-way shinkansen or limited express ticket can easily be 10000‰~. So think of it in these terms - you need to make 2 long-distance roundtrips in a week to ensure you get your money's worth. If you're willing to get up early and spend all day, you can even daytrip to venues like Osaka or Kyoto from Tokyo, just make sure you catch the last train back ~8:30pm.
FYI -Keisei Skyliner is superior to N'Ex. Shorter trip, better seats and fewer stops. If you're on the west side of town however, it's not as convenient as KeiseiUeno is the terminus; but not every N'Ex run proceeds to Shinagawa or Shinjuku, most terminate at Tokyo Station anyways. But if you're staying near Ueno-Tokyo-Kanda-Akihabara on the east side it's a much better choice.
In general, Tokyo transit is somewhat similar to London transit, in that there are several 'hub' stations where cross-town and intercity traffic meet, and JR interconnects with private railways. All of them are linked by the Yamanote loop line, and most by the Tokyo Metro as well.
West - Shinjuku - JR, Odakyu, Keio - mostly commuter and express routes to Kanto and Kansai. The world's largest and busiest train station.
South - Shinagawa -JR & Keikyu - commuter and express routes to Yokohama, Yokosuka, only stop on the Tokaido (south) shinkansen in-town besides Tokyo.
East - Tokyo Station - the 'Grand Central' of Tokyo. Terminus of both south and north-bound shinkansen, accessible on nearly every commuter line.
East - Ueno - JR + Keisei - the original Tokyo main station, only a few miles north. Ueno is the terminus for most north-bound limited express routes to Tohoku (Gunma, Iwate, etc) It is also a Tohoku shinkansen stop.
North - Omiya - JR & Tobu - interconnect for many north and east-bound services to the Tohoku region, Saitama and Chiba prefectures.
There are dozens of other large stations where multiple JR lines and private lines interconnect, often on adjacent platforms or across the street between two stations. But these are the big ones. A HUGE help today if you have 3G/4G cellular access in Japan, or even just wifi is to use the scheduling websites Hyperdia or Jorudan which are both available in English, and have multiple iOS and Android apps that use them as well. They allow you to select routes from point-to-point based on speed, cost, timing or even JR Pass-eligibility (eliminating the restricted shinkansens)
http://www.hyperdia.com/http://www.jorudan.co.jp/english/norikae/