1

What time exactly do you arrive?

Last train connection is at 0:10. See hyperdia.com for timetable. There is no direct bus to Shinjuku after that, but you could take a bus to Shibuya at 0:30 and a cheap taxi from there to Shinjuku. http://www.limousinebus.co.jp/en/bus_services/haneda/index

For the opposite direction, I believe, neither bus nor train will get you to the airport in time. Probably best to stay somewhere close to the airport. For places to stay see the bottom of this page. There are also some capsule hotels near Keikyu Kamata station.

2

Thanks bamse, for the information and links!

How much would it roughly cost to take a cab from Shibuya to somewhere in Shinjuku?

From this link you gave me (http://www.japan-guide.com/e/e2430.html), I see that the there is a 00:00 transport to Shinjuku. I just may be able to make that timing if I rush a little, but I couldn't find what that transport would be? I did a search using hyperdia.com, and it appears that anything after 23:51, and I will arrive in Shinjuku (JR) after 5 am! (Presumably because one of more of the connections would have stopped operating for the day.)

For the departure, say, at the worst case, roughly how much would the cab fare be to get from Shinjuku to Haneda?

Thanks!

3

Taxi will be round 8,000-9,000 yen.

To be honest, I'd just stay at one of the hotels near Haneda for both evenings.

If you are on a budget then First Cabin Haneda is a capsule style hotel but is quite nice, or there is a Toyoko Inn not too far away. Other options are listed on the page bamse linked.
http://first-cabin.jp/en/store_haneda-terminal1/

4

Just to clarify the taxi fare that acc mentions is for Haneda - Shinjuku. You can get a pretty fine hotel room for that amount...

From Shibuya to Shinjuku should be about 2000 yen, depending on where your hotel is. At daytime and without luggage it also makes for a fine walk...

I see that the there is a 00:00 transport to Shinjuku.
http://www.limousinebus.co.jp/en/platform_searches/index/4/214

I did a search using hyperdia.com, and it appears that anything after 23:51, and I will arrive in Shinjuku (JR) after 5 am!
Hm, I am quite sure when I just checked it showed me a 0:10 connection. Perhaps due to a difference in weekend/weekday timetable or I picked another terminal at Haneda. For comparison you could check http://www.jorudan.co.jp/english/norikae/ which allows you to specify a generic "Haneda Airport" (i.e. you don't have to pick a particular terminal) and sometimes jorudan and hyperdia assume different times required for making a transfer, so one or the other might not change connections with little transfer time.

As an example I found for February 3 from Haneda Terminal 1 a connection at 0:07 arriving at Shinjuku at 1:00.

5

If you want to party in the city it's worth getting there, but if you're just gonna sleep, just crash in the airport on the floor for a few hours...

6

Thanks for all the suggestions and links! :-)