You think Narita Airport is too far from Tokyo? As you check in at T-CAT (Tokyo City Air Terminal), only taking a subway for Suitengu-mae is enough. Although it costs 2,900 yen to take a bus for Narita Airport, here is less crowded than Narita. It is possible to go to Haneda from here, too.
Old town Ningyo-cho is close from T-CAT. You may buy some souvenirs here.