You have a lot of time and time to see Tokyo proper.
Time of day matters and whether you have luggage or not.

There is a once an hour direct subway train going to haneda airport. It's a long trip on one of the slower trains.

The two express trains from Narita into Tokyo are the Narita express (Tokyo station, Shinjuku) and the keisei skyliner taking you to ueno station.

Tokyo is pretty good about having lockers for you to store luggage.

My suggestion would be take the nartia express n'ex train to Tokyo station. Store your bag. Walk around the imperial gardens. Get some ramen. Sightsee a bit. Then go back and get your bag and take the yamanote line clockwise to the monorail to haneda airport.