Hi,
Oh God, please don't sleep on an airport bench. You are supposed to be enjoying a vacation. There are a number of cheaper hotels close to the airport, like First Hotel, Kanku Hotel Sunplus Yutaka, Izumisano etc. Some may have a free shuttle bus to the hotel, otherwise taxi fare is not too far or high. Check the typical booking engines like Hotels.com
Unfortunately if you are not taking the bullet train back to Osaka from Tokyo, a 7 day JR Pass would not pay off. But since you mention an extra day, one possible idea is to do a day trip to Hiroshima/Miyajima. If you start early in the morning, you can see the Peace Par/Museum and perhaps the castle or Shukkeien Garden, and about 3/4 a day to see Miyajima - it is one of Japan's top rated places. That would make the JR Pass cost effective as well as broaden your trip.
For Kyoto, be sure to take a day to see Nara as well - it is a must-see place as well. The multi-year renovation of Himeji Castle (Japan's finest) will be finished by then so it is also well worth your time.
Your comments about April 6th are unclear. At any rate, if you go to Hiroshima and make the 7 day pass worth it, it'd be best to bundle all your travel on bullet trains (which are the most expensive) within the 7 days.
For more helpful tourist info, try looking through:
http://www.jnto.go.jp
http://www.japan-guide.com
http://www.kyoto.travel/en
http://narashikanko.or.jp/en/
http://www.gotokyo.org/en/index.html