There's a lot posted that I would agree with. My Naked Necks (highly efficient feed-to-lay ratio breed) are great, so too the Buckeyes, also my Iowa Blues. I only keep one Mediterranean breed right now and they are THE best at foraging- my Penedesenca. I also find my Orloffs, Chantecler, and Jaerhons (which I no longer keep- great birds though) are also very active, efficient foragers. The Modern Games are always on the move here.
All the breeds I keep have access to twenty acres that they seem to thoroughly enjoy running around on though they don't utilise anyone near all of it. My Silkies & Polish like to roam, but I wouldn't say they are efficient or travel very far. Ditto for the Marans.
My best foragers of all are my Indian Runner Ducks and Guinea Fowl.