Bruges

Take a nice walk around the city. Rent bikes and bike around the city. Check out some chocolate shops. Have a beverage in the square. Climb the bell tower. Plenty of cool shops to check out. Take a tour of the chocolate factory. Plenty to do, I hope others will chime in also.
You will enjoy Brugge! :)

If the weather is nice, you can take a canal tour all around the town. There's also a very nice brewery tour, De Halve Maan (The Half Moon) if you like beer. Several nice restaurants. A medium walk from the center of town can get you to some windmills (one you can go up into to visit).

With only 6 hours I suggest, a tour of the De Halve Maan Brewery followed by the adventure of finding De Gaare Pub-then settling in, until you must leave. When you can return to Bruges for two nights, staying at Absoluut Verhulst and take the Pink Bear bicycle tour to Damme. We didn't have a good guide on our canal tour (he phoned in his diaglogue) walking about the city was better for us. And watch "In Bruges" before you go. Happy travels

Tour Markt Square - Basilica of the Holy Blood and Church of Our Lady are free. Climb the Belfort Tower - €8 Rent bikes and ride around the town and out to the windmills
Eat some Belgian fries, Belgian chocolate and Belgian beer De Halve Maan brewery tour

Definitely the canal cruise. And the fries with mayo are delcious. There should be one or two trucks in the main square selling them.

A canal boat ride will let you see the city, and is so beautiful. Market Square and climb the Belfry to see the city from above. Spend a couple hours just walking the streets sampling all the chocolate.

My husband and I were in Bruges for almost exactly 6 hours last Saturday (3/30/13). We missed the brewery (darn it, we would love that!) but purchased a guidebook at the train station with a walking tour of the town. I'm sure there are better ones available and I would recommend finding one before you arrive since you have time. Six hours was a good amount of time to wander the City and get out to the windmills, although we certainly kept moving, only sitting down a couple of times for a beer, waffle, and lunch. We did not do the climb to the top of the tower, it seemed a bit much for us finishing up a week in Paris. My husbands sunglasses are in the canal there somewhere.... so if you take any pictures on the bridges hold onto yours! ;) Have a wonderful time. We absolutely fell in love with this town.

Thank you all very much. Great info!!

This advice is great for me, too. I am taking a day trip from Brussels to Bruge in June. Thank you!

We love Bruges and are going back in a few weeks! We suggest everything that others have mentioned above. In addition, depending on the time you are there and you are into photography I would HIGHLY suggest the Photo Tour Brugge: http://www.tripadvisor.com/Attraction_Review-g188671-d2660058-Reviews-Photo_Tour_Brugge-Bruges_West_Flanders_Province.html Andy the guide is awesome and the tour was one of our favorite tours from our three week trip last year! I'm not into photography but my husband is and I enjoyed this tour! Oh and you can't go to Bruges and not go to the Dumon Chocolate shop!