Given your schedule (part of an afternoon, part of a morning), I think staying in Narita is perfect.

Maybe I've been to Japan too many times, but I enjoy just hanging out in a Japanese city, poking around in the stores, trying their local foods (there's always a local food), and just seeing what I can see. Except for the proximity of the airport and a few facilities meant to attract day trippers on stopovers, Narita is a very "real" Japanese town.

Here's my suggestion:

Reserve a hotel or ryokan in Narita. I stayed at the Ohgiya, which is a member of the Japanese Inn Group, but more traditional than some.

http://www.naritakanko.jp/ohgiya/englih.html

They come and get you from either of the train stations. (I took the Keisei line, which is only about 250 yen and 15 minutes.) My room, which had a private toilet and sink and a separate sitting and lounging area, overlooked a garden. Coming off a long flight at 5:00PM, I just wanted someone to feed me, so I availed myself of the o-furo and then took the option (extra cost) of a delicious tempura dinner. The next morning, I woke up about two hours before breakfast was available, so I bought a canned coffee from the vending machine in the hall and read through the tourist information that was in the room. Breakfast (also extra) was either Western or Japanese.

Afterwards, I explored the town on foot, eventually arriving at Shinshoji temple. The buildings themselves were standard Japanese temple, but the grounds were beautifully landscaped to mimic woodlands, and I had an extremely relaxing time strolling all the paths. At lunch time, I headed toward the main business district and found a restaurant specializing in eel located just across from the tourist information center. A nearby souvenir shop was having a sale on nemaki (the cotton kimono-style garments that make excellent summer bathrobes), so I took the opportunity to replace my old one, which was practically in rags.

The last thing I did in my circle tour of the city was stop off at a Jusco (think Target) to buy a travel alarm to replace the one I had forgotten to bring. I then stopped back at the inn to pick up the luggage they were holding for me. They gave me a ride to the Keisei station, and I resumed my journey into Tokyo, refreshed and ready to face the big city.

If you stay in Narita instead of going into Tokyo, you will still definitely feel as if you have been to Japan.