There are many parks around Doha with a playground where you could take your sons to have some fun. I have two boys too and they like playing in the parks. The problem is when summer comes, it is too hot to be outside especially during the day. As a solution, we convert one of our room into an indoor playground and put a swing, slides, and toys so they can play in the house. We put one-inch mats on the floor for safety reason.

Some malls also have indoor playgrounds for a fee. They also have children area with a lot of games and toys, even though most of them are designed for older children. Many chain fast food restaurants (KFC, McD, Burger King) have children play area, but it is usually too small.

Some times we take them to the beach for them to play wit the sand.

Hope it helps.