Only Apple knows how many iPhones are going to be delivered to each store, but based on various numbers we've heard, here is our best guess.
First, there are approximately 1800 AT&T Stores, and 164 Apple retail stores nationwide. Apple is limiting sales to 2 per person, while AT&T is limited sales to 1 per person.
We'd previously heard that Apple Stores would be getting somewhere around 1000 1500 units, with "flagship" stores expected to get more inventory. Based on user reports, some AT&T stores have been willing to give out numbers of inventory. The numbers have ranged in the 70-90 range for the few stores polled. Assuming these numbers are to believed (which is a big assumption), that places the first day of iPhone retail inventory at 400,000+ units.
To counter, one forum post claims that their AT&T store received 90 iPhones today (50 8GB and 40 4GB) with a large shipment also expected tomorrow. Forum posts are generally not very reliable sources of information, but is posted for interest. Despite these claims, it seems very unlikely that iPhones are already being delivered to AT&T stores, as Apple's security precautions to prevent premature release of the iPhone appears to be at an all time high.
Finally, there has been no official word on when iPhone mail ordering will start, but we presume mail order sales will become open sometime Friday (June 29th) night.