are there any (or several) shopping areas, perhaps looking for unique local wares?
I can't think of any "unique local wares" in Braine l'Alleud.
Shopping centres like this one - which has about 10 shops - sell the same sort of products you will find anywhere in the Western world: http://www.lavenir.net/article/detail.aspx?articleid=DMF20131128_022 (for location, see http://www.retaildetail.be/fr/magasins/jbc/jbc-braine-lalleud/1420-braine-lalleud/chauss%C3%A9e-de-tubize-shopping-manufacture-65).
The same goes for Passage Wellington (60 shops) in nearby Waterloo: http://www.passagewellington.eu/
In fact I think for the whole Brabant Wallon the only unique local wares would be food products such as honey, beer and cider.
We found a very nice place that sold Belgian lace. I apologize for not knowing the name. It was a few doors down from Leonidas chocolate shop. Best chocolates, by far, is at Neuhaus.
They used to be in the states, but are very hard to find.
Also, for anyone going to Brussels, please be safe. Lots of pickpockets and crime, especially at night.
My daughter and I did not feel safe here at all.
Carry a money belt, or very small purse.
We saw a guy shop lift from one of the stores; was very disturbing!