What should I request from Japan
In addition to a nice Japanese knife, you might also want to consider:
Iwachu (Nambu) Japanese cast iron cookware (heavy though)
Japanese water stones for sharpening your Japanese knife
fancy chopsticks with carrying case
bamboo cooking utensils
ceramic radish/ginger grater
sake or tea set (as recommended by Chemicalkinetics)
other traditional ceramic ware like rice bowls
Even if your mother can't make it to the traditional cookware districts, she should be able to find lots of really nice things at any of the big department stores (Isetan, Mitsukoshi, Seibu, Tobu, Marui, Takashimaya, Odakyu, etc., etc.). They all carry a wide selection of quality products and have lots of helpful staff.
I live in Japan and while knives seem like the obvious choice, and certainly they are, its not as easy to find the big names known in North America. Unless you go to the actual knife shops, you won't find Konosuke, for example, in every store on every corner. There are a lot of knives available, but always local knives, so unless your mom is going to the big knife regions, don't get your hopes up on a big name knife. Though you still can get a very nice knife for a nice price. I love my family name made petty knife.
There are a lot of decorative chop sticks for good price, bento boxes for good price, decorative fans, lots of pottery be it cups, bowls, sake sets, tea sets, etc.
Kappabashi Street in Tokyo is my favorite place to shop!
There you will find knives and wares (lacquered items, cups, teapots of various materials, sake-related wares, knives, spoons, chopsticks) and plastic food and on and on and on for many blocks on each side. Of course, harryharry, what you request from your mom is according to your interests and tastes, but Kappabashi has it all, except for food items. Those you will find at the outdoor market places all around the city.
Knives are definitely good. To some extend, it may be a good idea to get knife brands which are less well-known. The reason is that you can actually get many well-known Japanese kitchen knives for reasonable prices in US.
Japanese teaware or Japnese sake set are both good choices -- if you drink Japanese tea or sake. Conversely, maybe the tea and the sake themselves.
Are you into tabletop gas stove? What about an Iwatani stove?
Nice stove, but I think something got lost in the translation:
●The dining table which does well
●I am glad in a wallet
●Electricity is unnecessary
The pan which is full of 良 いこと.
Even if the interior of a room enjoying a pan, tableware have much one where they are particular about
There should be little one that is particular about a cassette cooker.
Because there is not the good cassette cooker of the design.
Though it is these days when design household appliances spread to here,
Though it is the leading role of the pan party around a friend
The design cassette cooker is ... still more.
The design cassette cooker which can say alone there is this.