The National Museum of Ravenna occupies the cloisters of the former Benedictine monastery next to San Vitale, and its collection ranges from Roman floor mosaics and archaeological fragments to Byzantine ivories, early Christian sculpture, medieval weapons, and 16th-century Flemish tapestries. It is a proper museum with a substantial and diverse collection, not a single-theme institution.
The archaeological section contains finds from Roman Ravenna and from the surrounding Emilia-Romagna plain, including material from the Po delta settlements. The early Christian and Byzantine section is the strongest: ivories, textiles, reliquaries, and mosaic fragments that complement what you see in the monuments outside. The medieval and later sections are less focused but include some good individual pieces.
The monastery cloister itself is worth the visit — a serene colonnaded space where the transition from exhibition rooms to open sky, from ancient to medieval, happens naturally. The museum is never crowded and is an excellent complement to the morning circuit of the UNESCO sites.