Vegas has some of the best and most polished shows in the country on the strip. You should take advantage of that by checking out at least one: I'd recommend Cirque du Soleil (O is my favorite) or a variety show.
There are a few fun rides/attractions on the strip as well if you have a bit of fearlessness in you. The Voodoo zip line at the Rio, the jump off of the top of the Stratosphere, and the roller coasters at NY-NY or Stratosphere are quite fun.
You have to hit up the Linq High Roller. It's one of the biggest observation wheels in the country with the option to include an all-you-can-drink open bar happy hour special for the entirety of the ride (about half an hour). Make sure to tip the bartender heartily at the very beginning so they know to keep the drinks flowing!
If you're into the outdoors and hiking I'd recommend Red rock Canyon which is about an hour off the strip. There are also guided tours with buses that leave from the hotels but I have no experience with them. They include even a day trip to the Grand Canyon.
One of my favorite parts about Las Vegas is just walking up and down the strip while stopping in all the casinos and seeing the various attractions at each (Bellagio fountain and garden, Caesar's Palace statues and decor, Aria circle, volcano show at The Mirage, etc...) while doing some people watching.
Finally, don't forget about indulging in all the fantastic food options on the strip. Some of the best buffets I've ever had, plus everything from fine dining to street tacos - don't miss Tacos El Gordo if you want some quality.
If you want to shoot some big guns, there are a few options for that as well. I tried Battlefield Vegas last visit and was not disappointed. It's a little expensive, but the fact that you can shoot everything from an MP5 to a Barrett makes up for that. Very seamless sign up and overall process with military veterans as employees that really add to the authenticity. Also allows you to roam around the barracks looking at and climbing in historic military vehicles. Shuttle service is provided to and from all strip hotels, as well.
