Taxi from Haneda to Shinjuku

Our flight is due to arrive at 10.30 pm at Haneda airport. We are a family of 4 with luggages. Would anyone know how much it would cost to catch a taxi to Shinjuku Citadines hotel? Or should we consider other options?

Would anyone know how much it would cost to catch a taxi to Shinjuku Citadines hotel?

Around 10,000 yen.

Or should we consider other options?

I would certainly consider more reasonable options, such as bus or train.

Bus connections:
http://www.limousinebus.co.jp/en/platform_searches/index/4/214

Train connections:
http://www.hyperdia.com/

Basics:
http://www.japan-guide.com/e/e2430.html?aFROM=2430_3011

By train you can do it for one quarter the price of a cab and most importantly I seriously doubt that you will find a taxi to take four people and luggage. We have had difficulty with just two of us with a suitcase and cabin carry ons each.