The last time I was in New Orleans (about 6 years ago), I stayed at the Hilton Garden Inn, to which I walked from the Amtrak Station. I seem to recall that the Hotel was fine.
A few years before that I was attending a conference at the Holiday Inn, which is also walking distance from the Amtrak Station. I had no choice where to stay since I was not paying, but I would have preferred the Hilton Garden Inn.
I believe that trolleys may get you close to the hotels from the Amtrak Station. Hopefully someone with better and more recent knowledge will chime in.