The only hotel right at the airport is the Narita Guest House, an uninspired and expensive place.
The Kirinoya Inn is an excellent place to stay in Narita city and is not far from the temple and the public bath. Although not much to look at from the outside, it is a very traditional Japanese inn on the inside, with tatami in all the rooms (picture) and an o-furo in the bath. The owner is interested in Samurai history and has on display many antiques. You can get a single room there for 5000 Yen. It's not an easy place to find. From the airport, take the Keisei line to Narita-shi. If you're good with maps, get one at one of the tourist information booths and ask them how to walk to the Inn. Or, take a taxi from the train station. If you call in advance, they may be able to pick you up at the train station. The distance from the station to the inn is about 1.2 kilometers (a bit less than a mile). The inn serves very nice meals and is next door to a convenience store which carries a good variety of discount priced beer and liquor. Although the proprietor speaks some English, the rest of the staff speaks only Japanese.
An option for budget travelers is Backpackers Fuji, which offers hostel-style rooms for under 3000 Yen. It's about a ten minute walk from the Keisei Narita station, not far from Jusco Department Store. Several readers have written in to praise this hostel as being "gorgeous", "super friendly" and "fresh". Brian notes that the 2700 Yen for the dorm bed also includes toast and coffee in the morning and free WiFi.
Several people have recommended The Azure Guesthouse, a dormatory style guest house with reasonable rates. It is a short walk from the train stations and has plenty of shops and restaurants nearby. Their web site is very informative. Several contributors have noted how clean and quiet the place is and how friendly and helpful the owner is.
There are a number of very dull hotels on the highway in the immediate area of the airport. You may be able to get a deal through a travel agent at places like the Holiday Inn. The Narita View Hotel charges 6000 Yen plus 18% tax and service charge for a single, but nearly twice that for two persons in the same room. Rooms at the Narita View Hotel can be reserved through the following telephone number in the United States: (800) 447-7462. The only thing to recommend the Narita View is the price of a single room. It is not a very nice hotel, the food is expensive and not so good. There is nothing to do, no place to walk to in this area. However, most of the hotels in the vicinity have free shuttles both to Narita City and to the airport.
Olivia Bennet reports that it is possible to stay in the airport: "I actually already had my layover there, and stayed in the airport overnight. The security people ushered the dozen or so of us to a corner of the airport and took our passport numbers, but it was no problem staying overnight."
David Loutzenheiser reports: "I stayed at the Narita Kikusui Hotel located roughly across from the Jusco in Narita. It was quite nice, with a buffet breakfast and most of the staff speak english. I'm not sure the price as I was with a group at the time. But the location is an easy walking distance to Naritasan Koen and the temple et al as well as convenient to both JR and Keisai stations."
Peter Morgan adds: "I just wanted to endorse the Narita Kikusui Hotel as a good one to stay. They are on the web via google at 5200yen/night, if you can book directly on the Japanese web page, otherwise about 5,600yen via travel agent in English. Good buffet breakfast at 630 yen. Free shuttle to and from the airport at the usual hotel shuttle stop."
George Bailey reports: "If you're a traveller with JAL and therefore being put up at the Nikko, you get a free breakfast but no free dinner, which can be expensive if you eat in the hotel. The best solution for a cheap meal to be eaten in the Nikko is, when you arrive, head for *departures* and buy snack food there, where you'll find a much greater variety of food and better prices, then head back to arrivals for the courtesy bus."
Rendell Davis suggests: "Perhaps the best choice in Narita for the single traveler is to book a room at the Narita Station Hotel through a JNTO Tourist Information Center ("TIC"), such as the TIC in Narita Airport Terminal 2. Although the rack rate at the Narita Station Hotel is 12,000 yen, the rate is presently only 5,000 yen (all-inclusive) if booked through a TIC. Not only does this hotel have a great location in Narita (only one block west of JR Narita Station), but also it provides free airport pick-up and drop-off. I found the hotel staff very friendly. The only downside is that, as with any Japanese "business hotel," the rooms are very cramped by Western standards. Nevertheless, each room in the hotel has all necessary amenities, including bath, TV, refrigerator, and AC (with individually-adjustable thermostat). The TIC rate here for a double room is 10,000 yen per night, which does not appear to be a very good a deal."
Another possibility is to stay at one of the 'Love Hotels' that seem to dot the landscape all over Japan. These places generally rent rooms for short periods during the day and early evening to those needing a private place for a liaison. They have a short time ('rest') rate for these transactions. They also have 'stay' rates for those wishing to spend the night. This runs about 3500 Yen. These places can usually be recognized by their gaudy exteriors and discrete parking. The rooms are often equipped with interesting decor for those with special needs or desires. There are a number of Love Hotels on the highway leading to Narita airport and in the vicinity of Narita City. You might try asking an airport taxi to take you to a "Love Hotel".