Regensburg's Museum of History is housed in a former Minorite monastery and covers the city's long arc from Roman fortress to medieval trading power to imperial free city. The Roman section is particularly strong — Regensburg was founded as the fort Castra Regina in 179 AD under Marcus Aurelius, and the museum has a substantial collection of inscriptions, military equipment, and everyday objects from the garrison. The Porta Praetoria, a surviving fragment of the Roman gate, is visible from the street just outside.
The medieval galleries cover Regensburg's peak as a prosperous trading city — the period when its patrician merchant families built the tower-houses that still define the skyline, and when the city hosted the perpetual imperial diet (parliament) of the Holy Roman Empire. The museum is not flashy, but it is solid and informative, and gives useful context to the buildings you will see walking around the old town.