Hey Brad - welcome to NCWW.
4x4s? Are you looking for that specifically, or 4" thick (16/4) material?
I suspect several places may carry 16/4 lumber (I know I have seen it at Capitol City lumber, but don't recall seing any at Anchor Hardwoods) but it depend very much on what species you want. I have seen poplar and I believe mahogany there at Capitol City - be prepared I believe these are in the $12-20/BF price range. These are not cut as 4x4s, but just thick lumber
If it is an outdoor project, then cypress directly from a mill (like the one I forget the name of, but on Hillsborough St, just west of NC Fairgrounds) might be your best bet.
I hope this helps
Henry