Sheki is the obvious day trip from Qax — or, depending on your itinerary, Qax makes the day trip from Sheki. The two towns are about 60 km apart and connected by regular marshrutkas. Sheki is the more celebrated destination, with its Palace of the Sheki Khans, its caravanserais, and its workshops producing the local silk and walnut halva. A day there and a night back in the quieter Qax is a reasonable arrangement.
The village of Ilisu, described under Things to Do, is close enough to be a half-day excursion rather than a full day trip — buses from the main station run five times daily.