Palais de la Mediterranée isn't the only choice in Nice, but it's a good one. Not far away is the Beau Rivage (www.hotelnicebeaurivage.com), which is closer to Vieux Nice. I don't love the Negresco because there's nothing immediately around it. Of course, some people may like it for that reason.

In the near-Nice category, I'd say you have two choices:

Grand Hôtel du Cap Ferrat (www.grand-hotel-cap-ferrat.com)
Hôtel du Cap-Eden-Roc (www.hotel-du-cap-eden-roc.com)

I think these two are on a different level than the near-Nice alternatives mentioned in previous posts.