Originally Posted by RichardInSF
How gutsy are you and what class are you flying? There is an 8:03 departure that gets in at 9:29. Otherwise, you have to catch the 7:07am that arrives at 8:35. Reserve your ticket no later than when you arrive in Tokyo, with a one night layover it's preferable to waiting and having the hotel do it.
The Limousine Bus is a fair alternative to the 7.07 train. At that time in the morning I would prefer it to the hassle of taxi and schlepp thru Shinjuku station with luggage.
There's a limo bus that leaves from Park Hyatt at 7.05.
http://www.limousinebus.co.jp/e/index_route.html
100 minute journey time - should be punctual on a Sunday.
Unfortunately, you can't use your JR Pass for that ...