Just a few ideas:
1. Go to the movies (ok, not very original, but it works). If you go to either of the UGC movie theaters, get a 5-movie card which allows you to watch movies at a slightly discounted rate (but watch out – the card expires within a couple of months, so if you don’t go often enough, stick to single tickets. The card, by the way, can be shared with other people.)
2. Pick up a book and have a coffee at Filigranes – Filigranes is a large (for Brussels standards) French language bookstore that in a very un-Brussels like fashion opens 365 days a year. Inside the bookstore, you will also find a coffee area (they also have wine and some sweet and salty snacks, like cakes and quiches). There is a small English books section as well. If you prefer an English-only bookstore, you can also go to Waterstone’s, which is not as cozy and has no cafe inside, but is also open on Sundays. This Thursday it opens late, until 23h30.
3. Visit a museum. If it’s Sunday, consider getting a Mont des Arts pass, which will give you access to seven museums around the Place Royale / Mont des Arts area for just EUR 11 (for adults. Children pay half the price). The Coudenberg site is worth a visit, as well as the Museum of Musical Instruments.
4. Go to the theater, concert or some other show. If you decide to do so on a whim and don’t know what to see, you might want to check out Arsene50, which is a service that offers same-day tickets for shows at a 50% discount. You can check the available shows online, but you have to go to one of the two box offices (Cinema Arenberg – Galerie de la Reine 26, next to the Grand Place; or the Flagey box office – Place Sainte-Croix) to purchase your tickets between 12h30 and 17h30 from Tuesday through Saturday.