Since you are probably getting the 7 day railpass for a 10day trip, it wouldn't be advisable to activate the pass on day 1, but ride regular fare trains for the first few days in Tokyo.

Transport from NRT-Tokyo:

Actually the Skyliner takes about 1hr 2minutes to reach Ueno from Narita.

The Keisei Limited Express takes about 1hr 15minutes, but with more frequent departures, drawback is that its a regular commuter train. But for only 1000yen its worth looking into if you are really crunching to save on yen.

Otherwise the Keisei Skyliner is good alternative.

But as mentioned it depends on your final destination in Tokyo, the Narita Express does make more stops in Tokyo, and the Airport Limobus will pretty much drop you off at the doorsteps to most major hotels in Tokyo, but both the Nex and airport bus will cost some 1000-2000yen more.