Does Unity have an Onclick type function for game menus?
Yes, there are several options. You could use the GUI 2.0 scripting interface which automatically handles input. Found here.
Or you can use GUITextures and then use OnMouseDown() in a script to act as a button click. Found here and here.
Both have their advantages. GUI 2.0 is slightly easier, because it takes care of most of the input handling, but GUITextures would allow you to be very precise and have more control over the button/ menu.