Salamanca (90 minutes west) is the most compelling day trip from Ávila — a university city of golden sandstone with a magnificent double cathedral, the Plaza Mayor that many consider the finest in Spain, and the Casa de las Conchas. It is worth a full day.
Segovia (70 kilometres east) has the most complete Roman aqueduct in the Iberian Peninsula, a fairy-tale Alcázar, and a cathedral. The roast lamb and suckling pig restaurants around the aqueduct are among the best in Castile.
Sierra de Gredos (40 kilometres south) is a granite mountain range with excellent walking in summer and some of the least-visited high sierra in central Spain. The Circo de Gredos, a glacial cirque at 2,400 metres, is a half-day hike from the Plataforma car park.
Madrid (90 kilometres east) is the obvious major city connection; the Prado, the Reina Sofía, and the Thyssen can fill several days if you combine the Ávila visit with a Madrid stay.