The nice thing about staying in Bruges is that, like many other tourist magnets, it was great in the early mornings and in the evenings when the day-trippers were gone or yet to arrive. I got up early, grabbed the camera, and wandered streets that were virtually deserted: a great time for architectural shots. The canals were mirror-like without the tour boats stirring them up, and the buildings in the Markt and Burg are more dramatic when lit up at night.
We also found that most of those day trippers didn't wander very far away from the Markt, Burg and some of the bigger attractions, like Church of Our Lady. There were parts of the old center where we encountered very few tourists at all during peak tourist hours.
I'm a big art fan so I'll leave most of those venues out but I'd hit Church of Our Lady (Onze-Lieve-Vrouwekerk), Jeruzalemkerk (that one is really interesting) and Basilica of the Holy Blood for church architecture. I'd also do Beguinage Ten Wijngaarde and Sint-Janshospitaal for their histories and architecture. There are some very important works of art in the latter that are well worth paying attention to even if art isn't your thing.
If you can fit them in, take a look around Sint-Salvatorskathedraal and Our Lady of the Pottery (Onze-Lieve-Vrouw-Ter-Potterie). You might also want to take in what's left of some of the Medieval city gates (Gentport, Kruispoort, Ezelpoort, Smedenpoort) and windmills along Kruisvest, close to Kruispoort.
But we never got tired of just walking and looking!