my flight the next morning leaves at 8:30, so yes, I'd have to be at the airport pretty early. The trick is though - I fly from the US into Narita, and catch my connecting flight the next morning via Haneda - quite daunting for a first-time traveler!
thanks again for everyone's help.
I think that itinerary makes your layover not as easy as it seemed at first...
First, connection between Naria and Haneda is very easy, because there are other people like you. There is the Keisei train that takes you directly to Haneda Airport (2-hr ride for 1560 yen, with possible train change somewhere such as Aoto Station) and Airport Limousine bus (75 minutes for fare of 3,000 yen, but no changes and no lugging around baggage). There is information service at Narita for foreign tourists to give you directions and how to do it.
The problem lies in the hours that you are staying in Tokyo.
Problem 1:
(1) There is no train or bus out of Narita after 24:00 and until around 7:00 the next day, making a stayover at Narita Airport impossible for you. (Of course, you can take a taxicab, if you're rich.)
Problem 2:
(2) Haneda Airport shuts down altogether from 24:00 to 5:00. I don't know if they allow people to lie down on airport benches and chairs until the next morning. The airport does not have sleeping rooms or restaurants open 24/7.
The best solution probably is to arrange for a hotel stay near Haneda Airport. You can go straight to the hotel, have a rest or look around (since Haneda is located in central Tokyo) and relax until the flight the next morning.
Personally, I'd prefer this to any other solution that may become nerve-wracking for a stranger in a strange land...