Lod Cook is a hotel that is run by the university and is on campus but I'm not sure about the rates. Look at the Hampton Inn or any other hotel on Constitution Ave; it's just off the interstate and not far from LSU. They have a lot of hotels on Corporate Blvd that are also pretty close.
Are you going to Bayou Country Fest?
We love ZBB. Have fun! Let us know if you need any other recs while you're here.