The ticket machines take plastic so that's not an issue.
For time in town I'd go with the Skyliner from NRT to Ueno. I like the area better with Ueno Park to kill time at being right there, Marunouchi is lots of shops, offices and crowded most of the day. Heading to HND I'd take the Keihin-Tohoku Line to Shinagawa and catch the Keikyu to the airport, The Keihin-Tohuku parallels the Yamanote but there's a lot fewer stops.