JRPass 14 days and hotel

You cannot use the JR Pass on non-JR trains, city subways or buses. You could use the JR Pass from Narita taking the Narita Express Train into Tokyo, and then pay regular subway fare to get to your station. If you will be in Tokyo for a few days, there is also a good subway day pass:
http://www.tokyometro.jp/en/ticket/value/travel/index.html#anc03
You must buy it outside of Tokyo though.
If you will be using the subways for 3 days, it is easy to recoup the costs of the subway pass. For 2 days though it is harder since subway fares are not that expensive - depends on your itinerary.
Another option is using your JR Pass for the JR Yamanote Line within Tokyo. The line goes to many popular tourist areas.

For Fukuoka, yes you can use the pass to go to Nanzoin on the Sasaguri Line (go to Kidonanzoinmae Stn). It's about 20 minutes from Hakata Stn. Nanzoin is one of the best kept secrets and most beautiful temples in the country:
https://www.youtube.com/watch?v=lT4VQFmHFyM

For other good Fukuoka info, see:

http://www.thejapanfaq.com/fukpic.html

https://www.youtube.com/playlist?list=PL7LcPcmoSg-j4RLa6iC7ayvBAbOn8-028