The Conrad is my goto hotel in New York, but $500/night is towards the upper end of their typical rates. While I have not stayed at the Hilton Millenium, based on all I have heard unless the rate differential is more than at least $100 less, you should go to the Conrad. I personally don't know anyone who prefers the Millenium to the Conrad and I personally would require a price differential of at least $150 to go with the Millenium.