Weather-wise, the story in Brussels is much the same as in London, Paris and Amsterdam: it can rain at any time of year, and the generally high level of humidity can also make hot days more oppressive: this may explain why some restaurants make a point of stressing that they have air-conditioning - some visitors may be surprised that air-conditioning is ever warranted in Belgium! That said, extremes of temperature are rare, even if the shoulder seasons May and September are the most pleasant.  Although  winters are not all that cold, compared with  the far North,  low levels of light  can be  depressing, especially when combined with  day after day of drizzle!

On very hot days between mid-July and mid-August, a good place to cool off is "Bruxelles Plage", http://www.bruxelleslesbains.be

On rainy days, you can still stroll and shop in the Galeries St. Hubert, Galerie Louise, City 2, Woluwe Shopping Center, etc. 

Brussels Weather - 5 Day Forecast