Originally Posted by freecia

You can search in Hyperdia for purely JR routes by unselecting the "Private Railway" options.

Here's a sample routing of Narita->Tokyo->Ueno routing from Hyperdia
HyperDia SearchResult

I'd probably take the Keisei Skyliner to Keisei Ueno when arriving at Narita and if the JR pass is still valid + you want to save money, N'EX from Ueno to Narita on return to airport. I'm usually tired arriving in Japan and just want to get to the hotel (even if I have a "travel high"). Your parents might feel the same and proper rest is important to keep their health up for the rest of the trip. You can exchange the JR pass at Ueno station the next day instead of at Narita Airport. The ticket office line at Ueno is probably shorter than Narita or at least more non-tourists who have quicker requests. Some of the offices which handle a lot of Tourist Pass exchanges only allow you to make a single seat reservation, too, so I end up having to visit a midori-no-madoguchi ticket office anyhow to finish my seat reservations.

My partner, OTOH, usually exchanges a national pass at Narita if he travels to Japan without me as he is more patient than me and familiar with the office at Narita. The familiarity of it makes him comfortable and he is more flexible about making advance seat reservations (I go to the countryside with sparse routings, he usually goes on more frequent shinkansen routes). Same goes with an extensive set of directions/video in English - If I suggest a more efficient Japan travel optimization, I usually include a video or directions to help explain so he can make an informed choice. That's fine, too, just something to know about your travel styles.