Brussles
Just 35 minutes from Lille Europe station on the Eurostar.  A return trip is about 35 EUR.

Bruge
About 2hrs from Lille by train. A bit tight for a day trip, but still possible.  Check Belgan rail for train details. 

Roubaix
Just 30 minutes by Metro or tram and only just over €3 for a day rover ticket.  Visit La Piscine - a museum of art and industry housed in an old swimming baths.