Fwiw
Given that in either scenario you're going to leave the Mini on continuously, you might want to consider using it as your home server, rather than just as your iTunes content server. By doing this, all of the computers on your network (I'm presuming there will be more than one) will be able to access the Mini and whatever is connected to it (physically or logically). Sure, you can accomplish this in a NAS-like fashion by connecting the Drobo to your router, but I think you'll find it easier and more useful if it was connected to your Mini.
Given that the connections from your iTunes server (the Mini) to the router will be wired, I'm curious as to why you would then switch to wireless from there to the aTVs. As I've posted in the past, the day I switched my household to a wired network was one of the best ever. 10G-rated cable is marginally near zero compared to cat 5 or 5e. Sure the aTV only sports a 100 megabit port, but that's today, who knows what the next hardware version will bring (as you may know, the current Macs all sport 1G ports). Anyway, switching to a wired network (if you can) will nearly eliminate the question of where to hang the Drobo storage, as the speed of the network will overcome a lot. That's much harder to do wirelessly - especially when signals get dropped, etc.
Still, if I were in your situation, I'd connect the Drobo directly to the Mini. It reduces traffic on the network and will also reduce the time before your music, movies, TV programs, etc. show up on the stereo/monitor connected to your aTV. Unfortunately, it looks like the Drobo only connects via USB. That's okay, but it would be better if you could connect via Firewire, as its sustained data transfer rate is much faster (even for Firewire 400) than USB2.
As someone said above, the Drobo seems too expensive for what it is - a RAID enclosure. I don't know how much data you want to store, but another route to consider is
http://g-technology.com/Products/G-RAID2.cfm. I don't work for these guys, but I have used many of their products and found them rock solid and nicely packaged with higher grade interfaces (e.g., Firewire 400/800, eSATA). For example, their 1TB RAID product lists for $449 compared to the Drobo enclosure (no drives) which at Newegg
http://www.newegg.com/Product/Product.aspx?Item=N82E16822240001 currently costs $445.99 after a $50 mail-in rebate.
One final note: If you plan on deploying multiple aTVs, then I think you should consider the impact on your network of using them simultaneously - especially if part of the network is going to be operated wirelessly.