It would be nice if the school had two teachers at each grade for you to choose from, and let you help pick, even though they don't let most other parents pick. Sometimes having two rooms helps because there is another kid that your kid really needs to be away from.
It's good if the teachers are aware that they set the tone for the children in term of how accepting they are of'the weird kid,' since your child will either be weird, or highly sensitive to the treatment of 'the weird kid.'
It would be nice if sometimes the children get to choose what kind of final product. Do they prefer to write a paper, record a video presentation, make a powerpoint, create a diorama?
Don't look for any of our favorite 'catch phrases' as the school world uses differentiation and clustering and other positive-sounding words without any appreciation of LOG, so that they are basically meaningless. The big acception is this: If you ask point blank about what circumstances require subject acceleration or gradeskip and they talk about susie, bob and harry in great detail, that would help.
If the school expresses glee at gaps, I would be impressed.
If the school talkes to you about 'some kids are working 3+ years above agemates' and we find ways to make school work for them.' I would be impressed.
If they suggest that you hire tutors/mentors to visit the child at the school during the school day, at your expense, with the child being excused from the subject with their agemates, I would be impressed.
Just keep in mind how rare Level III and up kids are, even though its 'normal' here. (1:1000, that's rare) Also keep in mind that 2E and LOG are totally cutting edge and usually will usually not have filtered over to the school yet.
Be sure to sit quietly and observe the possible teachers.
I have learned more from the folks who interviewed my son for private schools and evaluated him, than I did from our local tester who did his WISC III. And at much less expense. So I think the idea of 'visiting schools' is a good one if it doesn't disrupt your life too much.
Good luck,
Grinity