It's enough time to go into Tokyo and back again, but the cost (you will want to take the fastest, not the cheapest way with the time you have) will be about $40 each round trip if you take the Keisei Skyliner train round trip to/from Ueno station, which I'd recommend. Places you could visit include the Sensoji temple complex at Asakusa, the Akihabara electronics area, Ueno park and Tokyo national museum, or the Ginza area -- which is famous but less interesting, I think, than the other places.

The problem is that the first Keisei train (which is not a Skyliner) doesn't leave Narita airport until 7:49pm and you will likely be through customs/immigration before that, especially if you have checked your bags through. The first JR Narita Express is at 7:42am, not much better (and more expensive) and the one earlier JR train from the airport doesn't get in much earlier since it is slow. So your best bet if you can is to shower before immigration and then get on the train. I am not an expert on T2 but there are shower facilities although you might have to go through security to use them. Don't know how the AA club works at Narita, although others will certainly post about that.