Jim, I'd probably run 3 posts and piers under every other long joist which I would run from front to back (with the stairs to the upper deck being at the back) and two under each of the shorter ones that get the posts and piers. With the joists on 16" centers that would require 13 which is probably 12 or 14 more than the number of holes you'd like to dig.
The way I laid it out, that would put a post/peir at each corner, one nearly midway along each short side and five along the longest edge.
I'm kind of an over engineer, belt and suspenders sort of guy when it comes to this stuff so take that into consideration.
By the way, that lower deck platform measures out 7' 4-49/64" x 10' 11-27/32". If you'd like some help setting SU up to avoid that, I'd be happy to help. Send me a PM.
Irony: The opposite of Wrinkly