The Archaeological Experiential Museum is the best place to start in Vadnagar. It presents the town as a layered settlement, with galleries on its trade routes, religious history, fortification, excavated objects, and continuous human occupation. The displays include thousands of artefacts and connect directly with the nearby Amba Ghat excavation site.
This is not just a cabinet-of-objects museum. Its real value is that it gives shape to the town outside: the old fort gates, lake edge, Buddhist remains, temples, and domestic lanes all become easier to read after an hour or two here. Check opening days before coming, as museum schedules can change.