More than one way to skin this cat....

If you're nervous about getting up in the morning and getting to the airport in time to check in for your flight, then it makes sense to stay in the Narita area. You can still make it into Tokyo for an evening. There are trains to Narita city from Tokyo station and Ueno station, which run until about 11.20pm. (True, the express trains stop running much earlier than that).

My preference would be to stay in Tokyo itself. For such a short stay it probably makes sense to stay on the east side of town - book a hotel in Ueno. You can catch a Skyliner train from Keisei Ueno station to Narita airport in the morning.

An interesting and relatively cheap option would be to stay in Asakusa. This is a fun place to see - and you can get there quite easily by subway, which saves a few dollars.

Another option - book a room at the Royal Park Hotel, which is immediately next to TCAT. That puts you within a short subway ride of central Tokyo - and in the morning you can catch a limo bus back to the airport.

Another option - Leave your bags at Narita airport. Go into Tokyo and spend all night at a nightclub. Get on the first subway of the morning (subways running from 5am or so) and connect to one of the lines that takes you back to the airport (probably a keisei line) take a shower at the airport (either by paying or by using the free showers in the RCC) before your flight. But be careful - unless you are really tough, you are going to fall asleep on the subway in the morning and wake up in some god-forsaken corner of Saitama, having missed that flight...

Take your pick - happy to advise you further on any of the above.

BTW -- I used to commute on the line which is used by the Narita Express. Timetable disruption for earthquakes and typhoons are rare but not unheard of. Much more common is disruption due to a suicide on the tracks.