We are in a similar situation (Post-doc & gifted-school search)only that:
1. We are looking for anywhere in the world, not only US options
2. We know that our DS 6.10 is gifted but as he tested with WISC-IV without the extended norms we do not know how gifted he is (he hit the ceilings in some sub tests). With a 142 in the VCI and a GAI 140+ in a sub-optimal testing situation (he even ran out of the room once, hid under the table etc.) we realize that it may be good to retest in a year or two.
3. We have a few additional requirements- clean environment (air, water), balance in life (not terrible working hours)etc.
4. Both parents want to work (homeschooling not an option).

We are considering Boston (i.e Acera school), Stanford (i.e Helios new school), Canada (tricky thing is that in some parts the kids will be required to go to French-language schools, but then again, that may be a good thing)(Westmount charter school), Australia, Singapore (No 'perfect' option found yet). But all those places are not specifically for PG kids. I realize that you probably need to be more selective.

I hope you (we) can learn more from those with experience. Are you considering Davidson Institute? (Sorry not from US so I don't know if you may do astrophysics post-docs in Nevada).