If by "near to the station" you mean a place you can walk to, without dealing with streetcars and taxi scams, then I would suggest the Hotel Lafayette. While its Tripadvisor reviews have been "mixed," I had a real good experience there last March [i too arrived on #2 and left, some days later, on #20.] It was an easy 8-minute walk from the station, even with suitcase in tow, along broad, safe-appearing Loyola and Girod Streets. Hotel is older, but mostly renovated; and with its own restaurant and bar; and at the advance-purchase price of less than $100., the spacious, clean, quiet, and tastefully decorated fifth-floor room that I was given represented exceptional value for downtown New Orleans. The St. Charles street location, next to Lafayette Park, has also become much livelier in recent years - a top restaurant is across the street - and it felt safe, even at night.
