There is a superb art museum in Lille, the Palais de Beaux Arts. Train buffs have some interest in the driverless subway. It's a very long train ride from Brussels - if you can get a good fare, I'd even consider Cologne before Lille. But Cologne is worth the overnight. (I know your Brussels room is paid for.)
There are at least two new museums in Antwerp, the MAS and the Red Star Line [steamship] Museum. However, their main art museum is closed for years of renovation. I've never been, but there is a town abandoned (as a monument) for construction of the new Antwerp port, that's only open on Sunday. Also only on Sunday, the Deurne Volksmuseum in Antwerp - a glorified "New England Barn museum" behind a good bar. That's not worth a special trip, but I thought I'd mention it. You could consider doing Lier and Turnhout in one day - they're on the same train line and not quite worth a whole day each. Turnhout has a good waffel shop on the way into town (on foot) from the train - Het Wafelhuis Victoriestraat 47. Saturday is also market day in Turnhout, but you have to find out if they finished renovating the Grote Markt since my last visit two years ago. You didn't mention Leuven, which is worth a whole day. But all this is less fun on a cold windy day. (Leuven and Turnhout both have important Beguinages, as well as nice Grote Markts)
Check and see if Saturday is Market Day in winter in Mechelen. This was the most important city in Belgium just after the cloth trade in Brugge fell off. Mechelen's beguinage is only a memory, with fragments set into the walls of new buildings on beguinage-worthy twisting streets. Important cathedral, carillon school, and small museums. A brewery, but I don't know about tours.
Note that some important town halls (Antwerp, Leuven) only have interior tours once a week, on Sunday afternoon. Tickets at the T.I. I'd call in advance. Otherwise tourists can't enter these buildings.