A little river runs through Küsnacht. Follow it upstream, and you come to the Küsnachter Tobel, a deep valley through the woods. There is a path along the riverside, and this is a beautiful place to walk at almost any time of year. The river has several waterfalls, most very small, one quite big; some are natural, some were constructed to limit erosion. There is also a collection of "Findlings", large rocks left behind by glaciers at the end of the last ice age.
Several longer hikes start in the Tobel. most are signposted.
Küsnacht is on the eastern shore of Lake Zürich, and there's a path roughly along the lakeside from the Seehof, which houses the Gustav Jung Institute, northwards for about 1km. It goes through a small lakeside park, and past the landing jetty for the ferries. There is nothing spectacular to see, but it is a very pleasant walk, mostly along the lakeside.
In high summer you can swim in the lake from the park (free). There is also a special swimming area just to the north of this walk which has changing rooms, lockers etc but of course there is an entry fee.