No, you can't walk from the train station to the French Quarter but it is a five minute cab ride.
Check www.hotels.com and look for any of the following:
Le Richelieu Hotel
Hotel Provincial
Maison Dupuy
You should be able to get a room in any of these for $89/night or thereabouts.
Music: try to get to the clubs on Frenchmen Street (which if you stay at Le Richelieu is just across the street! Across Esplanade, that is). Also check the online music club listings in Offbeat Magazine www.offbeat.com to see who is playing in town that night. The recommendation for Antoine's Restaurant above needs a caveat: they have a dress code. So do Galatoire's and I think also the Windsor Court Grill Room: they are extremely expensive upscale places where ladies must dress nicely and men must wear coats and ties - if you're on a business trip you may be bringing these items in your wardrobe anyway, but if not, pass on those. For funky in the Quarter, try Coops on Decatur or the Acme Oyster House on, um....Poppagator, help? Is it Bienville or Iberville? or the Gumbo Shop on St. Peter. The best record store on the planet is The Louisiana Music Factory on Decatur across the street from House of Blues. Take home some New Orleans music!
Poppagator, can you email me? I've lost your e and can't seem to PM you. If you've lost mine too, it's on my web site. We can have a mini mudgather in New Orleans.