The Manchester Museum is the University of Manchester's natural history and cultural collection, housed in a Victorian Gothic building on Oxford Road. Its breadth is genuinely impressive: Egyptian mummies (one of the largest such collections in the UK), dinosaur skeletons, a vivarium housing live reptiles, archaeological finds from across the world, and a working beehive built into the exterior wall. Free entry.
The museum recently underwent a major redevelopment and added South Asia and China galleries, working with diaspora communities in Manchester to interpret their own collections. The result is more nuanced and interesting than the typical Victorian cabinet-of-curiosities approach. The building itself is worth noting: the Alfred Waterhouse-designed exterior is the same architect who built the Natural History Museum in London.