Where do you start? If you've not done so, do some research on the beers and bars (from books or online) before you go - - the diversity is (as I'm sure you know) immense, and the quality varies too - while there are quite a range of styles...which have little in common with the kind of beers readily available in the UK.
For what it's worth my favourites include
Rodenbach Grand Cru - a sour red (very refreshing on a summer afternoon, quite sharp, maybe a bit of an acquired taste)
St. Bernardus Abt 12 - which is a lovely, strong, dark, trappist-style (though no longer actually made my monks) beer (and based upon the same recipe as the beer regarded as being like gold-dust by some affectionados of Belgian beer, the Westvleteren 12 - although if you do manage to find a place selling that, I've found it can be a bit temperamental and needs to mature...). the Bernardus is far more reliable.
La Chouffe - refreshing and blonde
In Bruges, the two main beer bars with big menus are "Brugs Beertje"
http://www.brugsbeertje.be/ and (also in the centre of town, but hidden away down an alley) "De Garre"
http://beersay.wordpress.com/2011/05/07/de-garre-bruges/
I think Beertje is a little better, generally (and also slightly larger). There's another one, "Cambrinus", which has a decent beer selection but which, as a bar, really lacks character and is far too aimed at (English-speaking) tourists.
In Brussels, Bier Circus is a favourite, and fairly central
http://www.bier-circus.be/
While there are two branches of Moeder Lambic
http://www.moederlambic.com/bars/ one central one less so. Have only been to the further-out one, but it didn't disappoint.
I think there are many more options though....and I don't know Brussels so well
I can also recommend a (self-guided) tour around the (small and traditional) Cantillon Brewery in the inner suburbs of Brussels
http://www.cantillon.be/br/3_2 . You also get to sample some of the very fine Gueuze beers that they brew there included in the admission price
Avoid Jupiler and Maes - mass produced lagers than make Stella seem like champagne in comparison....
If you like Jacques Brel at all, there's a pretty interesting museum dedicated to him in Brussels - small but makes the most of the limited space...