All 4 hotels are within a block of Canal St (the border between downtown and the French Quarter) and within about 6 blocks of each other. So location is not really a factor in my mind.
The Windsor Court and the Roosevelt are probably two of the nicest hotels in town; I've seen 5 star ratings for both. The other two are solid 4 star hotels.
I've stayed at the JW and the Roosevelt myself. The JW has a more modern feel, the Roosevelt is very old-school decor.
You can't really go wrong with any of these choices.
ETA - the Roosevelt is part of the Hilton chain, under their luxury Waldorf Astoria Collection umbrella.