Maastricht

Yes, I've visited Maastricht several times (I have a family member on staff at the university hospital). Is it worth a few weeks? Well, other than being a rather pleasent city to walk around, it doesn't have many tourist "sites". I think there's a series of caves nearby that were formerly some kind of chalk quarry that you can explore, but I don't know too much about it. The neighboring Belgian province of Limburg is a pleasent place to hike, particularly the southern half. You're also not too far from the Ardennes/Eifel for even better hiking. The adjacent region of Germany isn't really on the tourist radar, other than Aachen. But if you like soccer, several of the top German football clubs (minus Bayern München) are based not too far away.

Overall, Maastricht is a very livable city, but I'm not sure it has very much to offer a tourist beyond a day or so.