If you like being near the Opera, I love the Park Hyatt Vendome on rue de la Paix, though it has a very different feel from the Grand.
If you like big, older hotels, what about the Meurice? (Very, very good restaurant, BTW.)
I love the George V, but I think it's several rungs above the Grand. Ditto Le Bristol and the other top of the line ones.
I would not consider Neuilly to be the heart of Paris, by the way.