Might be too late to reply, and i can't help you with the travel time (haven't done that drive), I can recommend the tour of the 9th ward where the levees broke. Most tour companies include that in a broader, overall tour of the city so the focus isn't JUST on the flooding (and the people who are rebuilding those neighborhoods don't suffer quite as much from the "fishbowl" effect; they are kinda tired of being curiosities). Personally I think it is still important to witness this historical event in person, if you have the opportunity. The scope and depth of the disaster really becomes more vivid when it is experienced first hand, and if we all knwo & care more, that education & emotional connection can only help to prevent such how events are handled in the future. IMHO. A city tour (including the 9th Ward) is a good intro to the city if you've never been there; use one of the established tour companies (Cajun Encounters, Historic N.O. Tours, Gray Line).
You are probably referring to Preservation Hall - definitely worth going to. Also for music get yourself to Frenchmen Street (or St. Claude if you like an edgier scene). For some nicer jazz clubs try Irvin Mayfield's and The Little Gem. Take the streetcar up St. Charles Ave. and see the Garden District (you can do a self-guided walking tour, there's one in Frommer's, or take an organized tour). For off the beaten path try exploring the Bywater area or Bayou St. John neighborhoods. They're very different areas but both have lots of history and some offbeat sightseeing. Good luck, have fun & let us know how it goes!