If there's a choice, fly into Haneda, not Narita
Haneda Airport is a lot more convenient for most travelers to fly into than Narita International Airport owing to the distance from Tokyo for both. It is not always an option. Delta for example only flies in and out of Narita while Cathay Pacific serves both airports. A train ride from Haneda to Tokyo Station takes approximately 28 minutes and costs around ¥580 ($6), while the train ride from Narita to Tokyo Station takes approximately 58 minutes and usually costs at least ¥2,600 ($25). If you need to, there are easy train connections between the two airports, just factor in around an hour of travel time to be safe (see the route map here).
HND is more convenient, considerably closer, and costs less overall to go into most of Tokyo proper.

Narita International Airport
However, for international arrivals and departures, HND usually has terrible flight times vs NRT. Therefore, check fares and schedules and see what works best for you.
Pros of arriving and departing at Narita International Airport
- Larger selection of international airlines that land and depart
- More public transportation options to central Tokyo than Haneda Airport
- Narita Express allows direct access to many major stations including Tokyo Station, Shinjuku Station, and Shibuya Station
Cons of arriving and departing at Narita International Airport
- Further away from central Tokyo
- Public transportation options are more expensive than Haneda Airport

| Year | HND Airport | NRT Airport |
|---|---|---|
| 2013 | +20,000 flights | |
| 2014 | Int'l. Services:+30,000 flights Dom. Services:+27,000 flights |
|
| 2015 | +30,000 flights |
~~lalala~~