FlyerTalk Evangelist
Join Date: Aug 2011
Location: Barcelona, London, on a plane
Programs: BA Silver, TK E+, AA PP, Hyatt Globalist, Marriott LT Plat, Hilton Diamond
Posts: 13,043
Narita airport is very far from Tokyo city centre. The major hotels in Tokyo all have "limousine bus" (not at all fancy) service to Narita for a charge.
Those who are more familiar with Japan are happy enough to take the train (quicker), but I wouldn't recommend it as a first timer - the massive train stations can be intimidating. And with all that luggage you'll want to take the bus.
You have to carry your luggage on board the shinkansen. However, you should look into the "black cat luggage service". For a very reasonable price they will move your luggage from hotel to hotel for you.