For a first time visitor I would recommend
Caesar's Palace - in many ways it comes closest to old fashioned Las Vegas ambiance, and the Forum Shops are nice to visit and walk through
Other places that are nice to check out and walk through are Bellagio, Mirage and Venetian (also nice shopping area to walk around).
For happening places to hang out with younger crowds, try Hard Rock, Mandalay and maybe the Palms. I don't like the stuff at MGM.
Best Buffet: Bellagio
Best shows - see if there is a headliner in town, or Mama Mia is very good, and if you never have seen a Cirque show check out "O" or "Mystere"