7 or 14 day pass

Well, April does not have 31 days.....

At any rate a 14 day pass would not pay off. With just your itinerary, a 7 day would not pay off either - but you can easily fill in the gap by also seeing some excellent areas close by - aside from Kyoto, be sure to see Himeji Castle - it is Japan's best - and after years and years of needed renovations, they will be done in March and would make an excellent day trip for you. Likewise, Nara is a must-see place that is worth half a day bare minimum and probably a full day to truly enjoy all that there is.

For the Tokyo area, some good day trip places are Nikko, Kamakura/Enoshima and Hakone. Going to some or all of those would be well worth it.

BTW you will be in Japan during Golden Week, which is one of the biggest travel times of the year. Some popular places may be quite crowded.

Whoops, yes, we arrive on 30 April. Thanks for the recommendations for day trips. Would a 7 day pass be useful to get to Kyoto and back and do day trips from Kyoto?

Yes, as well as the ones near Tokyo that I mentioned. The more long distance travel (especially by bullet train) you can do, the more the pass will pay off for you.

For getting to/from Narita, look into a cheap 1000 yen bus

http://accessnarita.jp/en/home/

or try the Keisei:

http://www.keisei.co.jp/keisei/tetudou/skyliner/us/fares/index.html

For other helpful info, see:

http://www.gotokyo.org/en/index.html

http://www.jnto.go.jp/eng/location/regional/tokyo/index.html

http://www.ar.jal.com/world/en/guidetojapan/city_information/tyo/see/akasaka/

http://www.japan-guide.com/e/e2164.html

For Kansai:

http://www.kyoto.travel/

http://www.ar.jal.com/world/en/guidetojapan/city_information/uky/see/central/

http://www.japan-guide.com/e/e2158.html

http://narashikanko.or.jp/en/

http://www.osaka-info.jp/en/

http://www.kansai-japan.net/en/