We just got back from a weekend trip into the eastern areas of Death Valley in an RV. It's only 2 hours out and a great experience for an alternative view of the area (Zabriskie Point is cool). Not too hot right now either. 30 mins west of the city is the Red Rock Canyon loop. An hour out to the east of the city is Valley of Fire which I recommend, and then of course you have the national parks in the south of Utah and Grand Canyon to the south if you wanted to make an extended trip of it. Hoover Dam also worth a visit if you have a car and is only about 30 mins out.
In the city itself and the Casinos? I have nothing else to offer as I hardly ever see the Strip.
Make sure to see the City Center hotel and casino complex. Penn and Teller at the Rio are fun.
(If you're traveling direct from London with BA or Virgin, try to book a seat near the exit. If you're in the back of the plane, you're looking at over an hour in the Customs line as the international terminal is still ****ty.)