1. The children have to play in their bedroom. The living room is not for them to monkey around in.
2. Steve likes to monkey around with old cars to see if he can fix them.

Compare to: monkey business; clown around; horse around; fool around. Monkey around emphasizes curiosity or the climbing aspect of play whereas horse around emphasizes the physical nature of play and clown around means to act silly. Fool around is the most general of these and could substitute for the other three.