Quiet family-friendly places for a weekend in Qatar?

For a quieter family weekend, I would look at Oxygen Park, Al Bidda Park early in the morning, MIA Park on a non-event day, or Al Khor Family Park if you do not mind the drive. For young children, I would prioritize shade, toilets, parking and an easy place to get food rather than choosing only by popularity. Going early usually makes a much bigger difference to the experience.