Watch the Bellagio water fountain shows from the balcony while enjoying great drinks and deserts
    show is every 15 min starting at 8:00 pm
    highly, highly recommended

The Ghost Bar at the Palms

    This is just off the strip but it is supposed to have an awesome view of the Strip
    (it's on the 50th-ish floor)
    I did not go up there (it just opened this past year)
    DO NOT GO ON THE WEEKEND!  At Xmas there was a $20 cover on Friday and Sat. 
    and drinks were $10. And there's a dress code.  I heard it was pretty small, too.

The Strip

   On the new section, where you are staying, a bunch of the hotels have outdoor shows
   that run every 15 minutes or so.  Its all part of the experience.  Walk by and check them out.
   Old downtown is where you'll see all the shots of Vegas from old movies the Frontier,
   the Cowboy sign, Freemont Experience.  Lots of low coin machines in that area.   
   AVOID driving downtown!!  Itll drive you nuts.  

Outside of Vegas
Red Rock Conservation Area

   West of city.  
   (Head West on Tropicana to Rainbow or Durango. 
   Head North to Charleston.  
   Head West on Charleston. 
   Its about 20 miles past Durango Rd.)
   Great short hikes, climbing, and bouldering
   Drive the Loop; its 13 miles and there are plenty of places to stop and get out
   ~40 min drive from your hotel
   When returning, instead of coming back the way you went (on Charleston/159), 
   follow the road. It'll go around the mountain past Blue Diamond and drop you
   back into Vegas south of the city.  An excellent drive.

Hoover Dam/Lake Mead

   SE of city
   Do the tour.  There are two types: the standard and the hard hat.  I've never done
   the hard hat one but its supposed to be super hip.
   ~40-50 min drive

Valley of Fire

   NE of city
   Very similar to Red Rock but with less people around and petroglyphs
   ~1 hour drive

Zion

   NE of city in Utah
   Beautiful, beautiful place.  Not sure of the conditions up there in the
   winter and its probably too much of a haul for the short trip you are on.
   Always a reason to go back to Vegas.
   ~3 hour drive