When people find out we live in LAS they almost always always ask how often we go down to The Strip, answer, every time we have company. If you have never been you gotta go. Something to remember is everything is a lot farther away than it looks. Wear comfortable clothing/shoes and stay hydrated (even in the winter.) The sidewalks are often crowed so just relax and enjoy the journey. In the summer you will often find entrepreneurs on the over crossings selling water. (this is not an authorized activity.) Speaking of winter, it gets really cold in Vegas in the winter...but it is a dry cold.
Suggestions are City Center, Fountains at Bellagio, Daquri Bar at Coyote Ugly in NYNY. M&M, Coke, Hersheys and anything else that looks interesting.
During your journey you will likely encounter TimeShare reps wanting to know how long you are in town for. Remember they are just trying to make a living like everyone else, i am always polite and often joke with them. If you are up for a high pressure sales pitch you may want to grab the free show they offer for 3hrs of your time. You will no doubt also encounter the porn slappers. Just keep walking. I ask a police friend why they don't shut them down because prostitution is illegal in Clark County. He said they are not selling prostitution and when you pay the $99 the girl will show up to your room and be offended after you proposition her, storming off. (with your $99...so you do end up getting scr**ed after all.) So just take in the sights, grab an adult beverage (you can drink while walking) and just enjoy yourself.
http://www.lasvegastourism.com/map_strip1.htm