Hmm, I don't know about your exact situation, but the JR East counters are only in the arrivals area of the airport. I don't think there's any reason why you can't reserve a N'EX ticket for the next day. It wouldn't be illegal or anything, but you would have to return to the airport to catch the N'EX, as it doesn't stop anywhere along the way.

First, though, whichever transportation you take, even the N'EX, you need to figure out which train station (there are dozens in Tokyo) your hotel is near. The information should be on your hotel's website under "Access." The reason you need this information is that different runs of the N'EX terminate at different stations. If, for example, your hotel is in the Shibuya district, you may want to take a N'EX that goes to Shibuya.

As far as taking the train from the city of Narita to Tokyo, first of all, there are two stations in Narita, JR Narita and Keisei Narita.

Taking the JR option requires one or two transfers, depending on the time ofday, and takes a little over 90 minutes.

Taking the Keisei commuter option, you need to figure out whether you are going to northern Tokyo (Ueno, Ikebukuro, Shinjuku) or southern Tokyo (Ginza, Nihonbashi, Shimbashi). If you want northern Tokyo, take the train bound for Keisei Ueno. If you want southern Tokyo, take the train bound for Haneda Airport.

In either case, there are possibilities for confusion with these local trains, especially if you don't speak Japanese. On last year's trip, I learned only because I understood the loudspeaker announcements that the southern Keisei train was going to terminate two stops short of my hotel and that I would have to get off and wait for another train.

So if it's your first time in Japan, I suggest figuring out a way to take the N'EX or the Keisei Skyliner, whichever is more convenient for your hotel.