The raised coop with run space underneath is how I built mine. That's their favorite space when it's 100+ degrees out. (often the case here in Texas)
basjoos is right, they will strip out all the vegetation from that run. I'd plan a way to put a roof over the run to keep precipitation out and minimize the mud.
Good job using real wire to secure the run and not just "chicken wire". That stuff is useless against predators. I would do something more secure to latch the doors against clever-fingered coons.
Oh, and
http://backyardchickens.com is great, if you can wade through the ladies' chatter of "oh, it's so cute and cuddly". There's a lot of excellent information there.