Do I need a 7 days JR Pass and other passes for the following itinerary

WilliamTay

Day 1 Day 2 and Day 3 will be exploring Tokyo.
Day 4 From Shinjuku station to Hakone using Romance car. Stay 1 night in Hakone.
Day 5 From Hakone to Mt. Fuji (by highway bus?) And then from Mt. Fuji to Osaka (Not sure how to go to Osaka)
Day 6 Osaka to Nara for a day trip and back to Osaka
Day 7 Osaka to Kyoto. Stay 1 night in Kyoto
Day 8 Morning in Kyoto. Afternoon travel back to Osaka. Midnight flight back to home from Kansai Airport.
What will be the best options for passes?
Thanks!

Tenjin

A JR Pass for such a one way itinerary like yours would simply not pay off. In your case just get regular fare tickets. For going to see the Fuji area, look into a Hakone Free Pass or Fuji Hakone Pass.
http://www.odakyu.jp/english/deels/

Regarding seeing Mt Fuji, if you mean taking a bus up to the 5th Station, you can do that but there is nothing there really - no view of the mountain since you are on it, no real scenery at all. You could however go to the Fuji 5 Lakes area which is very beautiful like Hakone.
http://www.japan-guide.com/e/e6900.html
The problem with that though is it would take about 2 hours to get back from there to Mishima Station, where you could board another bullet train to go to Osaka.
Another option would be instead to go spend some time on the Izu Peninsula, or backtrack a bit and see some of Kamakura/Enoshima.
http://www.japan-guide.com/e/e6310.html
http://www.japan-guide.com/e/e2166.html
http://www.japan-guide.com/e/e3117.html

Although a full JR Pass won't help you for this trip, there are some other tourist-friendly options that can save you some money. If you are flying into Narita Airport in Tokyo, then look into using the cheap 1000 yen bus.
http://accessnarita.jp/en/home/
You can also get a 2-3 day subway day pass for Tokyo:
http://www.tokyometro.jp/en/ticket/value/travel/index.html#anc03
Alternatively, you can get the Keisei+Metro Package:
http://www.keisei.co.jp/keisei/tetudou/skyliner/us/special/index.html

Given that you have so little time, and since you are already seeing Tokyo, you can largely skip Osaka during the day. After the temples of Kyoto close down around 5PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg and Abeno Harukas Bldg are wonderful. On your last day, you can easily go to Kansai Int'l (KIX) from Kyoto Station on the Haruka train (about 85 minutes), and use the Icoca & Haruka ticket for getting around Nara, Kyoto, and Osaka. The Icoca card has no real savings, but it's a prepaid card and much more convenient than lugging around coins and constantly putting them in ticket machines. You do get a good discount on the Haruka Ltd. Express train though.
http://www.japan-guide.com/e/e2359_icoca_haruka.html
http://www.westjr.co.jp/global/en/ticket/icoca-haruka/