Whereabouts do you live? Westbank, Metairie, Kenner, Gentilly? You're right about the roads, but most of the streets downtown are in pretty good shape... it's just a pain getting around the larger areas. I used to live in Algiers on the Westbank, lived in N.O. for about 10 years... if you have any questions, let us know!
For a starter bike, you can get any 26" mountain bike and bring it to a bike shop to have them tune it up... there's a few, I used to go to the one right off the Expressway and BelleChasse Highway.