Hakone to Narita
 

Can anyone recommend the fastest transit from Hakone to Narita? Will be going to Hakone for the first time and then need to catch an afternoon flight out of NRT... I assume I need to go back through Tokyo and catch the Narita express?

The fastest way will depend on what time and what location you are leaving.

For example, if you are leaving from Hakone Yumoto station at 9:18am on a weekday, the fastest way seems to be this route:

9:18 - 9:32
Hakone Yumoto to Odawara via Odakyu Tokyu Hakone #4

9:42 - 10:09
Odawara to Shinagawa via Kodama #632 Shinkansen

10:23 - 11:27
Shinagawa to Narita Airport via Narita Express #19

At other times, it will be faster to go to Tokyo and catch the Narita Express; still other time, fastest going to Nippori and connecting from Keisei Skyliner.

But generally, between 130 and 160 minutes from Hakone Yumoto to Narita Airport stations.

For the fewest changes, you could take Odakyu line to Shinjuku and then N'EX. However, N'EX from Shinjuku is not going to be the fastest way to get to Narita, because it takes a slow loop around southern Tokyo.

What do you mean by an "afternoon flight"?

Do you mean 1:00PM or 5:00PM?

If it's 1:00PM, you'd better follow hailstorm's route.

If it's 4:00PM, you have a lot more leeway. Make your way to Odawara somehow, hop aboard a Kodama Shinkansen, arrive in Tokyo, and transfer to the N'Ex. The trip should take approximately 2 hours, assuming that the next N'Ex is leaving fairly soon after you arrive at Tokyo Station.

You can book both your Shinkansen and your N'Ex at Odawara Station. All JR stations with booking offices are on the same computer system and can sell you tickets for any JR train or JR Highway Bus.

I would use Hailstorm's route.

4pm flight. Thanks for the input, folks. Appreciate it.

Agreed.
11.46am departure appears to get you to NRT terminal 1 by 1.58pm - with the changes described by Hailstorm above. Check Hyperdia for other options.

Kodama shinkansen from Odawara to Shinagawa or Tokyo is definitely faster but about Y2,400 more expensive than taking the Tokkaido mainline on the same route. So there is also a time/money tradeoff here, 36 min vs 80 mins, that's the extra cost of taking the fastest route.

All of the trains mentioned run very frequently so you can easily adjust to arrive at Narita at whatever time works best for your flight.

But, even in Japan, they are not 100% foolproof, so best to leave yourself some wiggle room.