Their hotel in New Orleans is where you stay if you get an invite. I don't believe they house invited guests in the other nearby hotels unless they are full (not likely these days). I do get many fewer invites from non-Nevada Harrahs than I used to. It helps to stay a few nights there every few years. If you are Diamond or 7*, you should be able to get a comped room at any Harrahs venue by asking. Also, log onto the Harrahs web site and login with your player number. You will be able to see all the offers you are elgible for at any time.
My experience has been that in a recession, it's not hard to get free rooms if you have a record of play, even if it's with another casino. I was in Biloxi last year and stopped by Hard Rock to play. They gave me an upper level card and offer of a room just for showing my Harrahs players card.