Originally Posted by
patchmonkey
As mentioned above, the limo bus to the Conrad leaves NaRiTa at 12:50. So if you're arriving at 7:30, you'll probably be out around 9AM (it took me about that long to get through customs and get my baggage the last time I arrived, but YMMV).
If you don't want to wait, drag your bag (I hope it has wheels) down to the train terminal in the station. Take the NEX to Tokyo Station. Then go get in a cab and take the cab to the Conrad. That trip will cost about 5000 yen, and it's not a bad ride at all. The NEX is all reserved, and you'll have a place to put your bag, and you won't be getting into Tokyo until 10:30ish anyway, so the rush will have died down a little.
My experience taking the redeye on SQ is that it often arrives early and there are few people going through customs at that hour. I've been out of customs well before 8:00am. Also, even if your bag doesn't have wheels, the luggage carts at Narita are designed to go down the escalator and you can take them almost to the platform escalator. It is more of a pain when you exit at Tokyo Station since there are no carts there.
Regardless, I agree with Patchmonkey's advice to take the NEX to Tokyo Station and then a taxi to Conrad.