Originally Posted by CPH-Flyer

Shinjuku is probablybetter placed for Haneda than for Narita. It will depend on exactly which hotel for the level convenience. You can take a limousine bus to Shinjuku Station from Haneda and then a short taxi hop to the hotel Or maybe your hotel offers a shuttle If you don't take the bus, you will be on commuter trains, which is not fun if you have luggage. Bus plus taxi is probably 2500 yen. You can take a taxi from Haneda, which will probably set you back about 8000 yen.

From Narita i would take the Narita Express to Shinjuku and a short taxi hop. Around 4000 yen total. If there is a limousine bus directly to your hotel, that's 3100 yen, before buying check how many stops it has before reaching your hotel. Sometimes it is annoyingly many. You can also get a fixed rate taxi here for 25.000 to 30,000 yen

I reality, I would as also suggested above chose by the flight schedule that suits rather than the arrival airport. But those were your transport options.