But why didn't we give them Kansas? Or, better yet, New Mexico?

IMO, Israel exists where it does because all the great powers knew two things:

1) There are a lot of religious sites in the region Zionists wanted control of and,
[perhaps most importantly]
2) We were bigger dogs than anyone in that region and so we could do it without costing ourselves much (except of course the 4 Billion/year indefinitely).