Mid Aug or Mid Sept

September would be preferable. So many Europeans take vacations for the month of August, and the weather in September might be a little cooler.

We just did a September trip this year. The temperature was nice, but be prepared for a bit of rain. Crowds in the major sites were still substantial.

I agree with David and Dav. August has good weather for going to the Belgian coast, to my opinion September is better for daytrips to cities in general, be indeed prepared for a bit of rain or some days with strong wind. Especially Bruges is still crowded during both months.

It's northern Europe, there's no way to know what kind of weather to expect, except for the wise advice above about rain.

I would stay in Ghent (or maybe Bruges) instead of Brussels. It's easy to day-trip by train in Belgium. Ghent is between Bruges and Brussels.

Mid September will be less busy as the children will be back at school. Personally, I think that Brussels lacks the charm and character of Bruges or Ghent, so I would take a train and use either of those as your base.

I would go with September, simply because your chances of hitting an uncomfortable heat wave are much lower than in August. Heat waves aren't common, but when they do hit, they can be absolutely miserable in a country where air conditioners usually aren't needed. At worst, the mornings in September might be slightly cool.

But perhaps if the heat does strike, that can give you an excuse to check out Belgium's lovely coast. I particularly like the town of De Haan.

I would prefer Brussels as a base because it is more central.
Belgium is not only Ghent Bruges and Antwerp, visit also Leuven, Lier, Tongeren, Spa, Huy, Robertville Lake, Malmedy, Andenne, St Hubert, La Gaume region, Bastogne and the Ardennes region.