I frequently stay at the Luxor, and there are various issues at play for you to choose from:
If you guys get free rooms at Harrah's, did you try any of their other properties, like the Rio?

If you stay at Mandalay or Luxor, you'd be accumulating play on their player card, which I don't believe is linked up to MGM/Mirage yet (I'm sure you've heard about the merger?). I'd forget NYNY, if you are a late sleeper just imagine the nightmare of the Coaster noise! Luxor will be cheapest of the places you list, but it's connected to Mandalay via the mall & exterior tram, so if you want to save money, Luxor is your choice. I always request a (free upgrade to a)corner room, which has a jacuzzi and is actually a suite - it's a good room to entertain in. If they won't comp you, or you don't want to pay for it, then I'd suggest a Tower room. If price is no object, rooms in Mandalay's newest wing (THE Hotel @ Mandalay Bay) are SWEET, but they run around $400 per night. There is no reason to stay in Mandalay's basic rooms, when Luxor is cheaper and so well-connected with the hotel...

Final considerations: Restaurants are superior at Mandalay, but it's a nice little walk through the Mall from Luxor, or a quick tram from the Sphinx. The Spa at Mandalay, and the Bathouse@ THE Hotel @ Mandalay are better than the one at Luxor, although the one at Luxor is pretty well equipped - just not as luxurious at those at Mandalay...