Brussels is generally dog friendly. Dogs are not ubiquitous, but it’s not uncommon to see them in restaurants. We had a great meal at Greenwich, Rue des Chartreux 7. The waiter told us all about his Mother’s dog who had just died (at 19 years old) and was so good to Fritz – giving him water and left-overs from the kitchen.
And there are also great parks!
The only thing that did shock me was that I had three cab drivers in a row refuse to carry me because of the dog (“it gets complicated with a dog” one said). A friend of mine who lives in Brussels said this is because the taxi service in the city is awful and that it didn't actually have anything to do with Fritz.