Just wanted to add my 2 cents. I'm also taking my family on our first award trip from miles, and we're flying into BRU in January. We're then flying to BUD on Wizz Air for 15 Euro, and then later on to BER via Easy Jet for around 25 E, then back to BRU via Easy Jet for another ~20E. We only had enough US miles for the TATL flights but with the incredibly cheap LCCs we wouldn't have used the miles for that itinerary.
I don't really recommend BRU as a destination, I find it sort of dull. We're flying in and out due to ease of booking the award trip, not because we love BRU. I would spend my time in Bruges or Ghent or, if you have a car, drive to the Zeeland province of the Netherlands and spend a few days in Middelburg/Veere. (I believe you can get from BRU to Middelburg on the train as well but not certain).
Hope this helps.