Omiyage is the Japanese social obligation of gifting. It's expected for travelers to bring omiyage when they go somewhere for hosts or when they return home for family, friends, or coworkers. It's best when the gift is a specialty product of the region, from which that the traveler is coming. Of course, in a country that values beauty in every detail, the omiyage has to be attractive and gift wrapped beautifully.
You may not know it yet but the omiyage you want most is the gomatomago. Goma means sesame seed and tamago means egg. Literally it is a sesame seed egg. It's a Tokyo specialty and previously available only at Tokyo Station. Last month I found it at Kansai International Airport (on a lone, small table in one shop on 3F), so you'll probably find it at Haneda and Narita airports as well.
When you purchase a box of gomatamago, they will put in this mod, black and white paper bag. If you tell the shop attendant it's a gift you'll receive a second paper bag, because they expect a bit of wear and tear on the first bag while you travel. The second paper bag will be fresh and crisp when you give the omiyage to its recipient.
There is no English anywhere on the box or shop displays. Sothis is the gift-wrapped box you need to imprint in your brain so you recognize gomatamago when you see it.
A fresh box of gomatamago. Insert sound clip of angels singing here.
Individually wrapped eggs
The white "egg shell" is made of chocolate.
Just past the shell is a thin layer of sponge cake. The black "yolk" filling is a mixture of sesame seed and sweet bean.
With Japanese-only packaging and a photo of black filling that might repel some, this is the best kept secret of Tokyo meibutsu (souvenirs).