In Australia we would just say "footpath", which is as non-specific as "pavement", so I think the Americans still win. If it is covered with grass rather than pavement (as many in Australia are) we would call it a "nature strip".

In America the pavement, of course, is the hard tarmac surface. This can be found, therefore, on the road and the, er, pavement/sidewalk.

This too makes sense as, I assume, the word pavement comes from the French pavé. See the Paris Roubaix bike race (two weeks this coming Sunday) for a lot more pavé.

Real natives of Baltimore (USA, not Eire) say pavement (though usually pronounced 'payment'), but sidewalk is understood.