What's the best way to get from Kyoto to Hakone? Since my airfare ticket included flight from Itami - Haneda for free, should I take an advantage of it? If I decided to fly, how far is Haneda airport to Hakone? And how much does it cost?
Thanks..

Easiest way to Hakone would be by Shinkansen to Odawara and Hakone Tozan line. 165 min and 12,050 yen. To use your ITM-HND flight, you'll first have to get to Itami (60 min by limo; 1,280 yen) and from Haneda either by bus or Keikyu train to Yokohama and JR to Odawara. The last routing takes about 2 hours and 1,720 yen to Hakone Yumoto. You can cut the time by 20 min by using Shinkansen, but it will double the fare.

Thanks alot! It's very helpful, but I'm a little confused though. It seems to me that it'd take me roughly about 4 hrs if I took ITM-HND flight (60 mins limo ride Kyoto-ITM, 60 mins fly time ITM-HND, 2 hrs HND - Odawara). Did I calculate the time right? You mentioned that I can cut the time by 20 mins by using Shinkansen, but it will double the fare?? Thanks again.

Also, do you think it's a good idea to stay in Kyoto instead of Osaka? I'm planning to take a day trip to Nara and spend 1 day in Okasa.

The two hours is to Hakone Yumoto, which is reached by slow but scenic mountain railway from Odawara. You'll only save around 20 min by taking Shinkansen from Shin-Yokohama to Odawara - not worth the expense IMO. I think the easiest way is to take Kodama Shinkansen from Kyoto to Odawara (just over 3 hours) and Hakone - just one change, compared with several with air/train option.
I agree that Kyoto is much the better choice for staying than Osaka. It's packed with historical attractions and eminently walkable. To Nara there's a faster Kintetsu line or slower JR.

Thanks again! I really appreciated your help. One more question though - Is it worth to buy a 4-day JR West Pass to travel in Kyoto, Nara and maybe Osaka? Can I use it to travel from Itami airport to Kyoto?

The normal JR West pass is only valid for areas west of Osaka, and won't cover Kyoto and Nara. There's what is called 'Kansai Area Pass' that is valid on ordinary (non-express) trains between Himeji and Kyoto, at 2,000 yen a day or 6,000 yen for 4 days. To use it for ITM to Kyoto run, you'll need to get to Osaka station by bus first and buy your pass there or get your voucher exchanged. But as ordinary fare Osaka-Kyoto is only 540 yen it's not really worth it for day one. Use it to get to Himeji castle, where one-way fare from Kyoto alone is over 2,100 yen.

Just came back from Kyoto, you could buy JR West Pass at Kyoto Station,with your passport. The pass covers Kyoto and Nara also.

Since someone mentioned JR West Kansai pass, I have a question.

The cheapest Haruka seat from KIX to Kyoto is 2980 yen. The JR West Kansai pass covers both KIX and Kyoto, but I find no mention of whether JR WEST Kansai pass can be used on Haruka Express on their web site or in several guidebooks I looked up.

Has anyone used this pass on Haruka express?

In Kansai area where Kyoto, Osaka, Nara, Kobe are located, private train companies do better than JR system. In general private lines are cheaper, faster, and more frequent.

It will be better to buy ticket every time you take a train, since you will have a lot more choices between two cities.

Between Kyoto and Nara, take Kintetsu. It costs you 610 yen and takes 48 minutes with one transfer, or add 500 yen and upgrade it to express that runs direct by 34 min.

From Kyoto to Hakone, everyone will take Shinkansen to Odawara and Hakone-Tozan. By the time your plane leaves from Itami, you will be in Odawara. Shinkansen runs variety of schedules, so make sure to take the ones that stops at Odawara but stops little in between. (All Shinkansen stop at Kyoto) It takes about 2 hours, by a slow Shinkansen it will be 3hours.

nickn,
JR west Kansai pass is valid for regular and rapid trains. If you wish to use limited express trains (Haruka is one of them), you have to purchase the limited express ticket that will cost you 1480 yen between KIX-Kyoto on top of the pass.

The normal fare between KIX-Kyoto is 1830 yen (plus limited express fee of 1480 for Haruka), so if you use the Kansai pass just for the ride, it will cost you 170 yen more.

http://www.westjr.co.jp/english/global.html may help you.