Yes the weather *should* be quite nice in early October. Yes the restaurant is expensive (like any luxury hotel), however there are lots of nice yet inexpensive restaurants just down the boardwalk a short walk away. Turn a left as you walk out of the hotel to the beach.

And yes it is very kid friendly. They even have a nice kids play room where I think they baby sit during the high season. But you can take your kid there yourself in October. Just get the key from the front desk. The only non-kid thing is the indoor pool in the spa area. That is adults only.