Do you recommend spending an additional night to check out Brussels City's Christmas markets?
It is a personality thing. Sure, if it would cost you no more, spending a day or more in Europe is always advised. Most markets tend to have a pretty commercial feel, you can find some nice local crafts and products, but also wade through stalls of commercial product. Food stalls can actually be pretty good for American tastes, so visiting one pretty much does it for me. I know some people plan a whole trip around a half dozen markets or more...that I really don't get...but then I plan trips around visiting breweries, so go figure.
Yes, Bruges has a market, so does Antwerp. If I had a choice, I would probably opt for Antwerp over Brussels (just for quality of the city), Bruges would be good as well if you are that way.