Kamikōchi, the most spectacular high valley in the Japanese Alps, is about two hours away by train to Shin-Shimashima and bus over the Kama Tunnel. The valley is closed to private cars and only open from mid-April to mid-November. It is the obvious day trip if the weather is clear; the walk from Taishō-ike to the Myōjin-bashi bridge takes a couple of hours along the Azusa river under the Hotaka peaks.
Hotaka and the wasabi farms (see Daiō above) are 30 minutes north by train. Norikura Highlands, with summer wildflowers and one of Japan's highest paved roads, is about an hour by bus. The post towns of the Nakasendō — Tsumago and Magome — are an hour or so south, reachable by train to Nagiso and a short connection.
For a longer day, Kanazawa is two and a half hours away on the Shinkansen via Nagano.