If you just want to drink beer, the lack of a car is in fact a bonus.
However, if you rent a car (even for a day), some otherworldly experiences may occur.
So, train only scenario.
Pick three cities to visit.
I'm assuming Brussels will be there, which means Cantillon is a must (it's practically next to the train station), as well as the classics. Moeder Lambic was mentioned (it has two locations, pick whichever is most convenient), and A la Becasse s worth another mention.
If you head out to Antwerp, you can't leave without visiting the Kulminator. Vintages here, and just about anything you can think of in terms of Belgian beer. Antwaerps Bierhuyske, Gollem, Patersvaatje,...all decent but cannot hold a cande to the Kulmi. Antwerpians used to drink a beer called "bolleke", which is an amber speciale belge by De Conink (now Moortgat). When done properly, this is wonderful. When not done wonderfully, it's a sad disappointment. Drink it in a place where they serve lots of it (Den Engel at the Grote Markt should be a safe bet, and a bit of a must-see anyways, pub-wise).
Bruges: be warned. It gets swamped with tourists over the weekend, and most of the known beer pubs will be full by the time you get there. Brugs Beertje, de Garre, Gambrinus,...everyone knows them, and the irony is they'll be drinking beers they could have got in any other pub. De Struise Brouwers have a tiny beer shop in the center as well.
If "any Belgian beer" will do, then you needn't necessarily seek out these specialist pubs: most Belgian cafés have a selection of beers which will appeal to most foreigners. You're unlikely not
to find most of the Trappists (bottled, occasionally one on tap), as well the ubiquitous abbeye style beers. Remember though that most Belgian pubs are "tied" to mega-breweries like Moortgat and AB-InBev, and this will translate into a monocline beer selection.
BUT hark! If you were to rent a car....being on wheels opens up a vast array of breweries and beer locations you'd otherwise miss out on.
De Struise Brouwers are only an hour's drive away from Bruges. The brewery is open to visit every Saturday between 2PM and 6PM and they typically have a fat dozen or so beers available on tap, often limited specials. This alone would be enough reason to rent a car.
A stone's throw away is the abbey of StSixtus, which itself cannot be visited, but it appears to be a Mecca of sorts for the beergeek. Shameless plug to myself, but you simply have to compare both venues for yourself
Make up your mind about the car first.
If you decide not to rent one, think of the trip as "city trip with a beer theme".
Having a car will probably mean it'll turn into a road trip slash beer haul.