Hi Lara,
I am not sure if it too late for any advice, but on the chance it is not.....
I am mom to five kids, and two were adopted from W. Africa, and one from Haiti. We have lived in Spokane for about 8 months. (Originally from W. WA.) I have not had any experiences with racism toward my children, and as a mom, I think I am quite sensitive to it.
When we first considering a move, I too fretted about the idea of moving my family to an area like Spokane. To be honest, I lived here the first few months with a feeling of only one foot in, and the other foot out, but my findings have been positive.
We attend church, and there are a few other black or bi-racial families at our church. We visited a few, so that we could find the best, somewhat racially diverse church. We are happy with the warm reception, and ALL my kids love it! (Note: At every single church we visited, we were warmly received, but chose the one we did based on the diversity there.)
Two of my 'brown' (That is what they call themselves, as they are learning their colors, and know they are not black.)

children are in the same class, and they have another AA girl in their class, as well as 3 Asians and a couple of Hispanic kids. Cultural or racial diversity isn't as great as other cities, but judging by my kiddos' class, I think that it must be increasing!
I say GO FOR IT!