How long are you going to stay? Are you looking for daytrips or weekend getaways?
For a great daytrip I'd suggest the mining museum in Bochum, probably the best of this kind in the world.
Luedinghausen is not far either and has one of the most interesting moated castles of the region with a good museum inside (most moated castles in the area are not accessible to the public).
Muenster is one of my favourite cities in Germany and also great for a daytrip from Unna. Interesting history and architecture (wonderfully rebuilt after 95% destruction of the city centre during WWII) but also a bustling university town. And it's one of the most livable cities in the world! Ok, I might be biased as I lived there for several years but it actually did win the www.livcomawards.com a few years ago.