Is it worth to purchase 7 days JP pass?

Hi there!

For a 7 day rail pass to be worthwhile you'll need to spend over ¥28,300 on individual JR tickets. Lets take a look at your projected costs:

1. Kansai airport > Kyoto: ¥3490, (75mins, 99km)
2. Kyoto > Takayama: ¥9680, (193mins, 314km)
3. Takayama > Odawara: ¥16910, (294mins, 559km)
4. Odawara > Tokyo: ¥1450, (36mins, 83km)

TOTAL: ¥31530 for 4 legs

As you can see you'll make a minimum saving of  ¥3230 with a 7 day Japan Rail Pass vs normal tickets. You will also have the flexibility to change plans during this period as all further JR travel will be totally free. For these reasons I can recommend the JR Pass for your trip.

Regarding hotels, you'll certainly have more budget choices if staying in Tokyo, but as you note you'll need to travel out daily to Hakone (which would be free with a JR Pass, but time consuming). I think in your situation I'd try and stay in the Hakone area to really get the most out of the experience - preferably at a hot spring hotel.

Please note that for Hakone the JR Pass will get you as far as Odawara. From Odawara you'll need to use the non-JR Odakyu lines to get up to Hakone itself. I recommend the Hakone Free Pass for this.

Hope this helps!