The Matheson Museum Complex gives Gainesville a local-history anchor beyond the University of Florida. Exhibits change, but the emphasis is usually on Alachua County, early settlement, civic life, natural history, and the people who shaped north-central Florida.
It is a low-key stop rather than a blockbuster, but it is useful if you want Gainesville to feel less like a college town floating on its own. The complex is close to downtown, so it pairs well with a walk through the historic district or a visit to nearby parks and cafes.