1 - Walk around gawking at the huge casinos and their elaborate themes. Seriously. That alone could take 3 or 4 days.
2 - EAT! - Some buffets are amazing! - Some are crap - Go to Caesars, Bellagio, Paris, Planet Hollywood Buffets. - Avoid Luxor, Excalibur, MGM, Flamingo.
The link above has some good tips. about 5 years ago
If you are in the mood for nature, head to the Red Rock Canyon National Conservation Area, only 17 miles west of the Las Vegas Strip (http://www.blm.gov/nv/st/en/fo/lvfo/blm_programs/blm_special_areas/red_rock_nca.html). The cliffs are stunning. The park has over 30 miles of hiking trails, but we usually just drive along the 13-mile scenic route, stopping at various vistas to take in the views. Once you get used to the stark scenery, there are lots of interesting desert animals and birds (come early in the morning or in late afternoon to see them most active), and the groves of gnarled Joshua trees look surreal. If you get hungry afterwards, there is the large Red Rock Casino nearby with decent restaurant options. 60 miles north-west of Las Vegas is the Valley of Fire State Park--also gorgeous and worth a visit, but it's more of a time commitment.
Along the strip, I like the Singing Fountains of Bellagio, which are free. If you time it right and climb the Eiffel Tower at the Paris casino across the street at dusk (there is a fee for going up the tower), you can watch the sunset and see the city lights come up for the night. Plus the fountains look VERY different from up there (and, again, it's a different experience of seeing them "sing" at dusk and all lit up in the dark).
If you are interested in the city's history, I enjoyed this guide to Frank Sinatra's Las Vegas (http://www.smithsonianmag.com/travel/Frank-Sinatras-Las-Vegas-200937811.html), and there is the Cultural Corridor to explore (http://culturalcorridorvegas.org/ -- don't miss the Neon Museum, where all of the most famous signs come to retire; early-evening tours are especially fun--you can see the signs in daylight and then again when they are all lit up).
If you are in the mood for art, Bellagio's Fine Art Gallery is small but impressive. Here are other art museums: http://www.theguardian.com/travel/2011/nov/16/top-10-galleries-museums-las-vegas
And, for thrills, there are the New York-New York roller-coaster and "the world's highest thrill rides" on the Stratosphere Tower (http://www.stratospherehotel.com/Tower/Rides). Enjoy! about 5 years ago
All of the above are great ideas. Other great ideas would include the Pinball Hall of Fame (http://www.pinballmuseum.org/), The Mob Museum (http://themobmuseum.org/), The Springs Preserve (http://www.springspreserve.org/) and The Neon Museum (http://www.neonmuseum.org/). almost 5 years ago