Stay at FS Cap Ferrat or elsewhere on Cote d'Azur?
I'm planning to spend four days on the Cote d'Azur at the end of an active two week trip at the end of the September, hopefully to relax a bit before returning to the stress of the real world. After going back and forth between where I wanted to stay, and whether I wanted to stay up in the hills or down near the water, I've narrowed my focus on the Grand Hotel du Cap Ferrat. The location is fantastic and I like that Cap Ferrat is supposed to be pretty quiet. My goal is to enjoy the scenery and relax, and this seems like a pretty good candidate.
But the end of September still has high-season-ish rates and having been burned too many times before I'm wary of paying north of a thousand bucks a night for a small, unremarkable room with no view in a very famous hotel, only to wish I had spent that money to more effect somewhere else. This will be my first real trip to the French Riviera and I don't have any experience to go on, so I thought of asking the collective wisdom of this forum...assuming I'm not going get a suite and instead spend just over 1k a night for a deluxe terrace room or maybe grimace and pay a bit more for a 300+ sq ft sea view room...is it worth it? Or should I spend that same money somewhere else nearby around Nice?