Hi Loanna,
For a 7 day rail pass to be worth it you'll need to spend at least ¥28,300 on individual tickets. I'll assume that you are arriving and departing from Narita when I calculate your costs:
- Narita airport terminal 1 > Tokyo: ¥2740, (62mins, 79km)
- Tokyo > Kyoto: ¥13020, (165mins, 513km)
- Kyoto > Tokyo: ¥13020, (161mins, 513km)
- Tokyo > Nikko: ¥5230, (121mins, 150km)
- Nikko > Tokyo: ¥5230, (117mins, 150km)
- Tokyo > Odawara: ¥3440, (35mins, 83km)
- Odawara > Tokyo: ¥1450, (36mins, 83km)
- Tokyo > Narita airport terminal 1: ¥2740, (58mins, 79km)
TOTAL: ¥46870 for 8 legs
As you can see you'll make a significant saving with a 7 day rail pass (saving ¥18,570) over individual tickets. You'll also do enough travel to make savings with a 14 day rail pass (14 day pass is ¥45,100), which you may want to consider if you are in Japan for longer than 7 days.
I have excluded other exploration around Tokyo - while you can use the Japan Rail Pass to use the JR system in Tokyo (maps) you may also choose to use the Metro system which is not JR.
For Hakone, from Odawara you will need to use the Odakyu Hakone Railway system to get up to Hakone as it is not a JR operated line. You can find out more on the Hakone free pass online.
We also have a blog post on day trips from Tokyo that you may find useful.
Hope this helps!