What Las Vegas hotel should we stay at between....?

Bally's, Paris, or Harrah's. The reason I have narrowed it down to these three is the deals that are being offered and there location at the center(ish) of the strip. I think it's really important to be within EASY walking distance to Caesar's, the Mirrage, and the Venetian. We are going during the week between Christmas and New Years (the 26th-30th) if that matters. I just dont know enough to say which one is the best. Any help would be great!