Teguise is small enough that you can see everything worth seeing in half a day on foot. The old square — Plaza de la Constitución, but everyone calls it the Plaza Mayor — is the centre of things, ringed by the parish church, the seventeenth-century Palacio Spínola, and a handful of low whitewashed houses. From there it is a short walk to the two old convents and the Cilla, the tithe barn. The Castillo de Santa Bárbara, on a volcanic cone above the village, is the one sight you need a car (or strong legs) for.
Time your visit to land on a Sunday morning if you can — the weekly market fills the village with stalls and is one of the biggest in the Canary Islands.