As far as restaurants go:
-Up the street, opposite Dior there is a trendy restaurant where celebrities from the Plaza often go, l'Avenue.
Down the street is place de l'Alma:
-One of the very best fish restaurant in Paris is Marius et Jeannette.
-Don't go to the others, especially not Chez Francis - it's dogfood. But ok for a cup of coffee, looking over at the Eiffel tower.
Across the river and towards the Eiffel tower is a newish museum, called 'Musée des arts...