In Nagano you should buy Soba, Apples and Miso Ice-cream. There are probably other products that the region is well-known for but this is all I can think of right now. Some of you may know that the many cities and regions of Japan are known for certain things and it is seen to be curious if you don't eat or buy the things from the region you are visiting.
There are a few souvenir shops near Hakuba train station. We visited these shops while waiting for our transport to pick us up at the station. There is a MacDonald's at the station.
I bought this Hello Kitty Mug at the souvenir shop in the Shiga Lake Hotel where I stayed. It shows Hello Kitty skiing, basically everywhere you go in Japan, you can buy Hello Kitty doing anything...even wearing sumo gear!