I criticize Mississauga's downtown but Celebration Square is neat. Glad that they left a bit of open space in one are rather than building another condo building.
If you want something to do then check their website/facebook to see what event they're having. In the winter, they often have free ice-skating. In the summer, I've seen ribest, summerfest, Viet fest, Muslim fest etc and everything's pretty much open to the public and usually free. They screen movies which is nice, why not take your kids on a summer day for a free movie of some classic from the 90s or before rather than spending $10+/ticket at Cineplex?
It's in a great location of course. Good way to spend the weekend with the family...go do something in Celebration square and visit the huge library right next to it. On the weekends, the downtown library usually has a sizable book sale, I've found some gems for less than a dollar. I always enjoyed being able to pick up a few books and read in the library as a kid. There's also a Chapters and a Playdium across the road. Mississauga Transit's main bus stop is beside Square One so all these places are right next to each other and you can spend the day here without a car. The city's done a nice job of planning its downtown for the family.
Of course there's only so much the city can offer for free, concert bookings would get expensive after a while. So I hope the city sets up more cheaper to organize activities in the future. Ribfest and Carrasauga are nice but more food related festivals that the city can fund through sponsors and of course the vendors would make it so much better, maybe a weekend market/flea market once in a while.