Should I get a 7-days JR passport pass?

Day 1 Narita to Hakone
Day 2 Hakone to Kyoto (2N)
Day 4 Kyoto to Tokyo
Day 7 Tokyo to Narita

Looking for the fastest route as we want to minimize traveling time for this trip. Appreciate ur advise. Thanks!

Day 1 Narita to Hakone

The fastest route is by Narita Express and Tokaido Shinkansen from Narita Airport via Shinagawa (or Tokyo Station) to Odawara Station at the entrance to Hakone. It will take about 4 hours from touch-down until you reach Hakone via this route.

You can look up connections here:
http://www.hyperdia.com/

Day 2 Hakone to Kyoto (2N)

By Tokaido Shinkansen:
http://www.japan-guide.com/e/e5206.html?aFROM=2158_5200

Day 4 Kyoto to Tokyo

By Tokaido Shinkansen:
http://www.japan-guide.com/e/e2363.html

Day 7 Tokyo to Narita

Depends where in Tokyo you will be based:
http://www.japan-guide.com/e/e2027.html

Yes, a Japan Rail Pass will be good value.

Thank u so much for the info. Having issues to find accommodation at those recommend hotels, all are full. Wondering should I change Kyoto to Osaka since it is just 30mins journey difference.

you can use hyperdia to check the transportation cost. as i used that, i found that actually i don't need to buy JR pass.

actually you can stay in osaka and make 1 day trip to kyoto.

When are you travelling? If it's within the next two months, places were booking out by July! The autumn season is extremely busy, especially in Kansai. If you can find accommodation in Osaka, then I would stay there - you're right, the trip is very short. Means you don't have to move all your luggage, too!

If you're travelling with a JR Pass, staying in Ōsaka is a good alternative to staying in Kyōto since the two cities aren't very far apart. You can choose a hotel in the vicinity of JR Ōsaka Station or JR Shin-Ōsaka Station - frequent connections to Kyōto via JR lines are available from both points. So long as you stick to JR lines and avoid Nozomi shinkansen services, the trips between the two cities shouldn't cost you anything extra.

The JR Pass pays off as said by Mr Uji. (The local superman)

As for accomodations during autumn period I could get accomodations for last year November when I was booking about August/September.

Try hotels nearer the train station. South of Kyoto Station especially. These are usually business hotels as they are not as near to attractions but near the station for layovers + convenience.

Options for cheap budget hotels include First Cabin, Piece Hostel, JHoppers, and K House. There are other accomodations near to Yasaka/Chonoin. But these are staying with residents and requires multiple email correspondence. Too much trouble for yourself, if you are travelling next month.