They definitely have distribution centers across the country. For instance, here in Boston, we get serviced out of Worcester, MA, and when I was living in NYC, they had someplace nearby as well (the specific city eludes me right now). I generally have the movies in my mailbox a day after they mail them.
The only time I notice any sort of delay is when I request a not-so-popular movie. My suspicion is that sometimes these get mailed from someplace not as close as Worcester, as they can take several days to make it to me.
Overall, though, I love the service, and would highly recommend if you like watching movies.