Arriving at NRT at about 1:30 p.m. on a Friday next month and staying at a ryokan near the Hakoneyumoto station. The ryokan has a last call for dinner at 6:00 p.m. A few questions:

(1) Any thoughts on whether we can make it the dinner cut-off, given the immigration queues/lines at NRT? Arriving in J off of a DL flight that's shown to be fairly reliable in terms of timeliness (from HKG). I've gone through immigration/customs at KIX before, but never NRT. Hyperdia shows that if I catch the 2:51 p.m. NEX, I'm okay and I'll make it in by 5:30. Anything later and I'm in past 6 p.m.

(2) Hyperdia is telling me to take the NEX to Shinagawa, transfer at Shinagawa to the Kodama Shinkansen, and transfer at Odawara to the Hakone-tozan Railroad. I'm guessing this is the most efficient method to get to Hakoneyumoto? We'll likely buy a NEX+Suica pass and the Shinkansen ticket separately at the JR ticket office at NRT. At Shinagawa, do we exit the gates and reenter the gates with our Shinkansen tickets? Or do we just make our way to the Shinkansen platform?

(3) Now for the typical tourist question... can one see Mt. Fuji on the Kodama between Shingawa and Odawara?

Thank you!

Should be no problem at all. You should clear immigration and customs in 30 to 45 mins. So your 2.51 train looks fine. In addition, it may be possible to take a later train. Here's what I get from Yahoo! travel:

15:15 Narita Express 32 to Shinagawa - arrives 16:23
16:34 Kodama 671 to Odawara - arrives 17:01
17:21 Odakyu Hakone 37 to Hakoneyumoto - arrives 17:36

I don't know why, but Hyperdia seems to have some flaws when it comes to planning trips to and from Narita airport.

I would agree. Via Shinagawa is the way to go. It's a very easy station to change trains at.

The JR travel center at the airport will sell you your NEX+SUICA pass and your Shinkansen ticket all together - and make the seat reservations for both trains. Simples!
When you get to Shinagawa, you won't exit and re-enter. Just go directly to the Shinkansen part of the station. When you get there, you'll need to go through a second set of gates to get to the Shinkansen platforms. (Yes. it's like a station within a station).
For the Hakone Tozan railway, you will need to exit the JR station and enter the Odakyu station. You can buy a ticket or a pass there, or use your SUICA cards. I'd probably use the SUICA, but some of the experts here might know of a pass that would be worth buying. It may depend on what other travel you're planning in and around Hakone.
IIRC, the usual "view from a train" comes into sight somewhere after Odawara (between Odawara and Shin Fuji). However, I guess there may be places where the mountain shows its face before then.

1. Easily if your date of arrival is not during Obon.

2. Shinkansen is faster than the alternate route on Odakyu's Romance Car. Here's a map of Shinagawa Station for reference. You can either stay use the N'EX ticket to leave the station and then use the Shinkansen ticket to enter the Shinkansen station, or stay inside the station and deposit both tickets to get through the Shinkansen ticket gate.

The Hakone Free Pass will be worth it if you plan on doing the Hakone loop. The pass includes free rides on Tozan railway, cablecar, ropeway, boat and bus.

3. You will have a better view of Fujisan from Ashinoko in Hakone than at Odawara station.

Miracles do happen, but if you're going in August, it is unlikely that you will see Fuji from anywhere.

That's exaggerating things. Certainly there's a strong chance that Mt. Fuji will be hidden in a white haze on a typical August day. However, the mountain emerges from the clouds, even in August. I don't know what the probability of a clear view on any given day may be, but I recall some hotels had packages that provided refunds in the event the mountain didn't come into view during the guest's stay. (Of course, they had people watching very closely on cloudy days so that they could avoid paying out - even if the mountain was only visible for a brief moment). It doesn't take a miracle to see the mountain in August.

If the OP manages to visit Hakone after a typhoon blows through, then the view of the mountain will be spectacular.

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Thanks for the replies! Didn't know Hyperdia was squirrely with ex-NRT trips and that Yahoo had a comparable train planning feature. Will check that out. Will report back after we make this trip.

We'll only be in Hakone for the night and are getting back into Tokyo (Shinjuku) the morning after (the SO really likes Hakone for some reason) so we'll probably just take the Odakyu line back--no need for a Hakone rail pass.

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One more thing. On our NRT-HKG leg (we're flying HNL-NRT-HKG-NRT-HNL and using a stopover in NRT that makes up the basis for the OP), which I think departs at 6:30 p.m., will it be possible to see Fuji-san after we clear the cloud covering? If so, ant suggestions on which side of the plane we should sit on?

This is just a guess - I haven't flown that way in many years. I think there's a chance you'll see Fuji from the plane and I would guess that it is most likely to be visible on the starboard side of the aircraft. Some of the usual suspects on this board are regular passengers on that route, so I expect they'll weigh in...

I've seen Fuji on HKG-NRT, so I presume it's visible going the other way as well.