Drew,
Get off the plane, grab your rental car and head for the nearest
"In-& Out" Burger! Order the Double Double, Animal Style and get one of their shakes!!! My trips to Vegas doesn't start until I have one of those!!!
Make sure you visit "Old Vegas" and have a steak at Binnion's. After dinner walk around old town, there's usually a lazer show going on, music, and a bunch of Vegas characters running around!
During the day head to the hills as someone already suggested, you'll be amazed at the differnce from town to wildlife. Evenings, head to the strip, I don't gamble either at least I'm not very good at it, but I've been known to spend my allowance ($20) on a slot machine. Also bring some good walking shoes, you'll find yourself going from attraction to attraction.

Winterun