The big three-armed piece is the upper intake manifold. It's probably actually a plastic rather than metal. You could have a leaking upper intake manifold gasket or a cracked or warped manifold. It could also be something less expensive, but chances are good the shop will want to remove the upper intake to get a better look. If they go that far, it probably would make sense to have them replace the lower intake manifold gasket as well.
You could ask the shop if they have a smoke machine for identifying vacuum leaks. I'm not sure they are very common yet, but when used properly they can greatly speed up the time it takes to pinpoint a vacuum leak.
-Rod