Puzzle feeders, scent games, and short training sessions tire minds as well as bodies.

Rotate toys weekly so novelty returns. Food puzzles turn meals into problem-solving time and slow gulpers down.
Hide treats around a room for a scent hunt, or teach a new trick in five-minute bursts. Mental work reduces destructive boredom.
For cats, add vertical space and window views. For dogs, practice calm settle on a mat after play so excitement has an off switch.