A worthwhile trip from Nagano is to see the snow monkeys at
Jigokudani-Yaenkoen near Shiga Kogen ski area. I did a day trip from Hakuba to see the snow monkeys, lunch at the old sake brewery at Obuse and the Zenkoji temple in Nagano. There are a couple of tour companies organising tours from Hakuba for skiers having a day off from the slopes and I'd imagine that there would be similar tours offered from Nagano city.
Obuse is a nice little town with traditional buildings and it's not too far from Nagano city.