We will be arriving in Brussels on a Sunday morning and plan to spend Sunday and Monday in the Brussels and Bruges area. What type of things are open on a Sunday afternoon?
Restaurants should be open, but some only for dinner. Most stores will be closed. There may be a Sunday market, although these generally start to clear out by noon. I'm not sure about stuff like museums and monuments...
In Brugge, you could take a canal tour. I believe the boats run every day, from 10 am - 6 pm (March - November). We did the tour last year and it was an enjoyable 1/2 hour.
Most museums and monuments in Belgium tend to open on Sundays and close on Mondays.