Custom Menu in Themes not working even in Twenty Eleven theme

I suspect that the problem here is that, on your remote test site, you haven’t created any custom menus. Try creating one or more custom menus, and then the “Theme Locations” meta box should appear, enabling you to assign your defined custom menus to defined Theme locations.

As is shown in the Codex entry for Appearance -> Menus, the “Theme Locations” meta box is disabled if no custom menus are defined:

Appearance->Menus Admin screen with no custom menus defined