Oh Vegas..
I like off the strip hotels so have previously stayed at the Las Vegas Hilton the last couple of times in LV, now the Las Vegas Hotel. Old and glamourously appointed.
Things to do:
Shop at the Premium brand marts (or whatever they are called), amazing discounts on brand names.
Visit the Hoover Dam, take a tour, follow up with a helicopter tour of the same facility.
Catch the lion show at MGM
Have Bouillabaisse at the Provincial at Paris Casino.
Shop at a Walmart, it's an experience
Walk the strip while drinking a Daiquiri from a large coughtail class hanging around your neck.
Hire a Mustang, drive back to LA. (tip, when choosing a hire car from a major chain I.e. AVIS, get a car with CA plates not NV plates, then there won't be a relocation fee!)
Get crazy and gamble ;-)
Vegas is full of things to do, with a hire car you will enjoy your stay far more unless your motive for being in Vegas is gambling. Last year wife and I ate at an authentic Mexican Taco joint we found while driving aimlessly around Vegas, we shopped at shopping malls again found while aimlessly driving around and didn't regret 1 minute of having a car.