Fez sits in the middle of a particularly rich slice of northern Morocco. The standout day trip is the combined run to Meknes — Moulay Ismail's seventeenth-century imperial capital, with its great Bab Mansour gate and vast underground granaries — and the Roman ruins of Volubilis, half an hour further on, where the mosaics are still in situ in the open air. Both can comfortably be done in a single day from Fez and grand taxis run frequently from Bab Boujeloud and the bus station.
Closer in, Sefrou is a small market town in the foothills of the Middle Atlas, famous for its June cherry festival and a quieter glimpse of small-town Moroccan life. Rabat, the present-day capital, is a longer trip (about two and a half hours by train) and probably better treated as an overnight, but it is doable in a long day if you start early.