My favorite thing to do in Nagano is visit the Zenkoji temple, right in the heart of the city. It is decked in history, and you will find many shops selling different Japanese food and charms to protect from evil spirits, and many people basking in its wonders. Remember, if you get there at the right time, you can request to walk through the dark hall under the temple. This is said to be a rebirth exercise, and you will remember it forever.
Quick Tips:
Of course, I would recommend at least knowing some common Japanese phrases before starting your trip. They will go a long way!
Best Way To Get Around:
I would actually suggest walking around Nagano, and when you do need a rest, buses and taxis are the easiest things to take.