We have a free day in Brussels after having toured the city. I am looking for suggestions of where to go for a day trip via the train. We have already been to Bruges, Antwerp and Ghent and loved all of them. Any ideas?

Lille?

Paris or Amsterdam in the fast train.

You have many day trip options, it all depends on your interests and whether you want to spend the whole day away or just part of it.

If you're interested in WW I sites and museums, the Ieper (Ypres) is the perfect choice, visit the Flanders Fields museum.
http://www.inflandersfields.be/

If you'd like to put a toe into Germany, you can easily get to Aachen to visit the old town and the cathedral. http://www.aachendom.de/

Leuven in an attractive university town, close to Brussels, easily reached by train. You can explore on your own or take a guided tour.
http://www.leuven.be/showpage.asp?iPageID=1775

You could visit the close-in suburb of Tervuren to take in the very good Central African museum. You can get there by the #44 tram from the Montgomery metro stop.
http://www.africamuseum.be/
Or go out to the Chateau de la Hulpe for a long stroll around the grounds, a visit to the Folon museum on the grounds and a snack at their cafe. http://www.fondationfolon.be/index_en.htm

Paris is always a good day trip option (although check ahead for strikes that may complicate your plans).

In the Netherlands, besides Amsterdam, you could day trip to Leiden, Den Haag, or Delft.

I've day tripped to all of those destinations (and many others) from Brussels and enjoyed them.

Pick up a copy of the weekly English language newsmag The Bulletin and check the "what's on" section. You may find something special going on right in Brussels.

Thanks for the replies. I have checked them all out and think we may do Leuven. A few years ago we went to Ypres and it was great. Looks like there are several things to see in Leuven. What is the name of the station where we will get off the train. I see the tracks on a map and it doesn't look like it would be a long walk to the town center. Anxious to see the town center and the Beguinages. Thanks again.

Leuven is a perfect choice.
The name of the station is Leuven.
To get to the centre you walk out of the station, cross the street and walk straight along the Bondgenotenlaan. It's an easy 10 min. walk towards the Market Place that houses the most beautiful city hall in Belgium (IMO).
Enjoy!