Photo: Alessandro Antonelli, CC BY 3.0 via Wikimedia Commons
Many Italian cities had defensive walls in the Middle Ages, but few in Lazio still have such an imposing and well preserved one. Rieti's walls were built in the 13th century and enclose the northern side of the city centre; they were not needed at the southern side, enclosed by the Velino river, a natural defence. Unfortunately, you can't get on top of the walls, so the only way to visit them is to take a walk along viale Canali and viale Morroni, which border them.
It maintains the original 16th-century wooden doors.
17th-century fountain at the centre of the square.
It consists in a display of sculptures, coins, goldsmithery and objects from the prehistoric, Etruscan, Hellenistic and Roman periods, including an iron age urn found near Rieti.
St. Dominic church has an architecturally significant convent, well worth a visit. It develops around the Blessed Colomba cloister, with a beautiful Italian-style garden and a portico decorated by frescoed lunettes illustrating the life of the blessed Colomba. At one side of the cloister, there is the St. Peter the Martyr Oratory, a small chapel that houses an astonishing fresco of the Last Judgment, painted by brothers Lorenzo and Bartolomeo Torresani between 1552 and 1554. Sadly, it is almost impossible to visit the oratory and the cloister, since it's part of the military area of an Italian Army barracks (caserma Verdirosi), and the military allows touristic visits only on special occasions (e.g. "giornate FAI"). This is a real shame, since it is arguably the most important fresco in the whole city!
The so-called geographical centre of Italy might seem like a gimmick to attract tourists, but Rieti was nicknamed "Umbilicus Italiae" ("navel of Italy") even in Roman times. The exact point is at St. Rufus square, recorded by a multilingual plaque and a monument which locals call "caciotta", as it resembles a round cheese.
It's a small alley that perfectly represents the typical features of mediaeval cities, with arches, ladders and narrow passages. It's not the cleanest spot in town, although it has been repaved.