A full 7 day JR Pass would be economical. You can start using it from Narita, as well as the JR Yamanote Line inside Tokyo - it goes to many of the most popular places. I presume you are staying in Asakusa since you keep mentioning it. The most popular site in the area is the Sensoji Temple:
https://www.youtube.com/watch?v=SwjnQDjwaPQ
The Sky Tree is also very nice - very pricey, but best view anywhere when the weather is clear. The best time to go up is just before sunset, and watch the day turn to night. It is a popular time though and may be more crowded then (you can buy the tickets anytime and designate the time you want to go up though - buy them when there is less of a line).
For Hakone, you might look into a Hakone Free Pass:
http://www.japan-guide.com/e/e2358_008.html
If you can and are interested, in Tokyo try to see Harajuku and Meiji Shrine on a Sunday (Mar. 29) to see the wild youth fashions and popular shrine.
https://www.youtube.com/watch?v=3tY7jPFhTBM
For Kyoto, do your best to squeeze in at least half a day to see Nara - the Great Buddha at Todaiji Temple is like the Taj Mahal of Japan.
For more info, you might look at:
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 Kyoto:
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
For Hakone:
http://www.japan-guide.com/e/e5200.html