There are tons of places you can reach within a day's driving from Las Vegas. In addition to the great destinations listed upthread, don't overlook scenic areas in Vegas's backyard: Red Rock Canyon, Valley of Fire State Park, Lake Mead, Hoover Dam, etc.

My standard advice for people considering wide-ranging trips in the Western USA, particularly for those coming from overseas, is to be serious about the distances between destinations. Carefully evaluate how much time you'll spend driving (or otherwise in transit), how much tolerance you have for driving, and how much time will remain for actually visiting the places you arrive at. More road trips are spoiled by attempting to do too much than too little.