That's a really nice gift. You don't say where the couple is actually flying from? I think that may have a big impact on your choice. (And also availability of awards on the dates they want to travel might limit your choice).

That said, looking at a random date (Feb 18, 2014), and considering only non-stop flights from East coast airports, here's my first stab at an order of preference

First choice:
JFK-NRT: NH (777) - First
IAD-NRT: NH (777) - First

Second choice:
JFK-HND: AA (777) - First

Third choice:
IAD-NRT: UA (777) - First

Fourth choice:
BOS-NRT: JL (787) - Business
JFK-NRT: NH (777) - Business
IAD-NRT: NH (777) - Business
JFK-NRT: JL (777) - Business
JFK-HND: AA (777) - Business

Fifth choice:
EWR-NRT: UA (777) - Business
IAD-NRT: UA (777) - Business
JFK-NRT: DL (747) - Business


Caveat: My experience on these routes is out of date and limited, so I will bow to the others here who have recent and extensive experience. But I hope that my first pass will stir up some opinions.

Once you also throw connecting flights into the mix, the possibilities mushroom. I'll mention one possibility:
Outbound with KE or OZ via ICN to KIX (or FUK or another regional airport in West Japan)
Inbound with one of the above airlines from NRT to East coast (non-stop)

EDIT: I forgot about AA's flight to HND. So I've added it in.