Be early!
Haven't been there since Katrina, but parking seem to be kind of limiting. You would definitely have a long walk still even early enough. Probably would definitely take the valet. My preference at the time was to be able to walk to the paddock and perch myself at the top step of the stands behind the entrance to the walkway to the track. You can see the whole race up there except for a small section where the tote board blocks view.
Don't recall restaurants, but if you want to watch from inside (clubhouse and enclosed grandstand), I would try to make reservations as soon as possible.
The clubhouse and grandstand does have outside overlook access to the paddock which is a must see. Then visit the quads, and party on Royal and Bourbon streets.
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