Joel Sherman of the NY Post outlined exactly how the Yankees plan on replacing him this offseason. It involves trying to trade pitching, specifically A.J. Burnett, either straight up for a DH-type or for salary relief before trying to sign one. They will also explore trying to trade a young starter, specifically Phil Hughes, for a young, controllable bat.
Only if the Yankees fail to deal Burnett or Hughes (and possibly one of the minor leaguers if the right deal presented itself), then they will look to the free agent market for the Johnny Damon or Hideki Matsui types.
I wouldn’t completely rule out them trading Freddy Garcia for a bat either.
There is about a month before pitchers and catchers report. I expect that they would like to have this all wrapped up before then, but I doubt they will rush to do anything too soon.