We went to each school and put ourselves in Mr W's shoes in the rooms the place had and tried to imagine him there.
He was about on par with your kids and thus was so far beyond his age peers and so easily got along with much older kids, that we struggled with finding the right place. When we visited different locations, the stark difference in abilities between Mr W and his age peers made us very uncomfortable for him.
The non-academic daycares and the Montessori schools did not work for Mr W for long because he would retreat into his own world and he came to resent the lack of intellectual stimulation and the fact that his classmates could not talk.
He progressed from nanny, to in-home care with a home-school family, to Montessori (2y-3y), and then a one year acceleration into an academic PreK (3y to now). He could easily do the K program but we would not know what to do with a 4 year old who is ready for first grade.
In general, I'd look for a place that seems flexible and which has a lot of intellectual stimulation and where kids of mixed ages are together. I'd let them give their spiel then tour the rooms when the kids are there, looking at what the kids are doing and saying and what kinds of toys and stuff are there then seeing in your mind how the fit would be. Ask to see classes 1-2 years older than your kids. You are trying to find out if the staff can see and think on an individual kid basis and not in terms of rigid categories. I would not bring up GT at this point.
The other part of the equation is taking your child to the center and seeing what they gravitate to. Take them into the various rooms and then ask which one they like. It will then be obvious which one is a fit. Mr W sat down in the Pre K room and started working on a 30 piece puzzle and did it, read a few words out loud, etc. He sold himself.
We then brought up acceleration, asking what their criteria were, etc.
This is one approach.
