What's open on Sunday in Belgium

Stores (including grocery stores), banks and office-based businesses are closed. Restaurants, cultural and leisure sites and museums remain open.

Will breweries be open for tours?

You can tour the citadel in Namur. It's not far from Dinant.

Shops and some restaurants will close on Sundays, but some shops may remain open at railway stations and in very tourist oriented areas. Many museums and historic sites will be open on Sundays but closed on Mondays. A few museums and historic sites may close on Tuesday and not Monday - check the specific website to be certain.

In Belgium in general opening hours of shops is hard to say as there is no fixed rule when they have to be open or not.

In Bruges grocery stores like Carrefour (smaller ones inside town) are open every day. Fashion shops, (maybe a few exceptions) are closed on Sunday as well mostly large grocery stores / shopping malls outside town, but smaller ones in small places often open Sunday morning. Bakeries in general at least Sunday morning and I think many also early afternoon.

Places like Bruges (1 hour) and Ghent (1/2 hour) best to reach by train from Brussels.

Very few breweries open their doors for regular visits to the general public, due to insurance and sanitation regulations. For example, you can't even visit the abbey at Chimay, barring one of the rare open houses they hold, or unless the visit is business-related. Many breweries, particularly the smaller ones, run restaurants and guesthouses where you can sample the wares along with delicious food pairings. Here's one of Europe's best-kept secrets: Belgium's beer is well-known, but the food in the country is almost uniformally excellent. Even the food at the cafeterias in the Carrefour supermarkets is delicious!

There are a few exceptions, the most well-known being De Half Maan in Brugge, but increasingly, the brewery is moving most production to the modern (untourable) facility outside of town center, leaving the old brewery more of a demonstration center.

If you're a beer fan and you have a car, make a plan to visit St. Sixtus. Like all trappist breweries, you can visit neither the abbey nor the brewing facility, but this is the only place the in the world where you can reliably purchase the legendary Westvleteren beer. If you don't pre-order, your purchase is limited to a 3 pack, but St. Sixtus also operates a guesthouse. Now, to tell the truth, having sampled the beer, I think it's Holy Grail status may be mostly attributable to the difficulty in obtaining it. It is very good, just not quite as other-worldy good as its reputation (and I'm not sure if I just had a bad batch, but I found their blond ale all but undrinkable). But driving to St. Sixtus at least gives you a good travel memory. The abbey isn't located directly in the town of Westvleteren, but in the middle of nowhere down a barely-paved agricultural lane.

Batagne? Where is that? Or did you mean Bastogne??
In Brussels many things will be open on Sunday's, quite a few restaurants and some museums. Shops will be closed except some food shops in the morning. Chimay might be more difficult.