I can't speak for CSI since I've never really followed those shows, but they film NCIS in LA and insert D.C. area shots when necessary. It's probably cheaper for them to do it that way, so I imagine New Orleans will do the same.
Would have been my guess, too, but just read an article that said they will be filming in NO. IMHO, that won't last...too expensive.
Btw...saw Scott at CBS Upfronts the other day. Looked GREAT. Took 'congrats on new show' humbly, per usual. Classy guy. Wish him lots of luck. Will certainly tune in...and love the accent he used in pilot!