Actually, Maya does tell you what keys are free. In the Hotkey Editor, hit the "List All" button and you'll see the "Unmapped" column on the right.

Personally, I've gone in and scripted custom marking menus, I know there's a marking menu editor as Stwert mentioned, but I find I have more freedom this way. Definitely check out the marking menu editor though. Or maybe you'd be more into custom shelves.