KitKat chocolate with Matcha or Sake flavor , plum wine or If it's something from Kyoto, I would suggest SOU SOU textile shop.
However, I would recommend 「KAKI-NO-TANE」for a unique souvenir.
It is one of the popular Japanese snacks and it goes well with beer or some alcohol.
KAKI-NO-TANE is consisted of soy flavored rice crackers and it has several different types of flavors, such as wasabi, pepper, amongst others. The name comes from the fact that the pieces of crackers look like a seed (種 tane) of the persimmon (柿 kaki).
Interestingly , they have different flavors according to the region.
For instance, they have cheese flavor in Hokkaido , Matcha flavor in Kyoto , Okonomiyaki flavor in Hiroshima.
It might be fun if you look for a regional KAKI-NO-TANE places to places a whole part of Japan !