Mandalay Bay has the best pool area on the strip. Caesar's has the best location of the hotels you listed. The Mirage is nice but it's not the best at any one thing.
Does the trip your wife won include the hotel and those are the three option? If so, I'd go with Caesar's just because of the location.
My first choice for Vegas would be Bellagio though. Best location on the strip. Fantastic hotel. Nice pool area. But it won't be the cheapest.
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