A lot of schools will say they differentiate. When they say this, you need to ask for specifics about how they do this. What does it look like? What are the more extreme amounts of differentiation they've done, and what did those look like? How specifically do they differentiate for a child working three, four, five, or more grade levels beyond his age grade? Do they provide extra work or different work (important difference there)? Do they have a way to provide actual instruction at different levels? Or do they just toss the kid a workbook and call it good (and this is actually better than many schools do)? If the school can't give specific, detailed answers and examples for these questions, or if the staff become defensive or dismissive, those are important clues about how the school will deal (or not deal) with your child. If they do provide strong, detailed answers, then ask if you can see some of these situations yourself.
I would also ask what the school's policy on clustering is. Does the school cluster the highest kids together in one class, so they can have academic peers? With a PG child, even at a gifted school, there may well not be any real academic peers for many or all subject areas, but there may be one or two who are close enough to be a good social and/or academic fit for your child. Be very, very wary of a school that says they don't need to cluster or that all of their kids are very gifted!
Everyone has given you good advice, but I'll reiterate that a private gifted school is often not the panacea that we all hope for. Our own experience was that our local private gifted schools felt that they were for the gifted, so what more could we want? They said all the right things, but they did not put any of it into practice. I now wish that we'd asked much more careful questions and listened for the specifics--then we'd have known to avoid the school!
