Twentse Welle is the main museum of the Twente region, covering both industrial heritage and natural history. It's one of those regional museums that exceeds expectations — the collection is well-curated and the industrial machinery on display gives a visceral sense of how textile production actually worked.
The museum is particularly good on the social history of the Twente workers, with reconstructed domestic interiors and photographs of factory life from the late 19th and early 20th centuries. Worth two hours of your time. Industrieplein 4, Hengelo.