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Mine: Blackjack and free drinks, what a combination.
And if you have never seen the Hoover Dam, make the trip. It's quite a sight.
On the weekends you can play blackjack with dealers dressed as celebrities. It's a blast.
I also like to check out the statue of David at Ceasars palace. It's an exact replica of the real one, even carved from the same stone. It's very impressive when you see it in person.
Galleria is some pretty prime shopping (I'd RATHER shop in Georgetown, but Las Vegas is WAY closer....) and the shopping venues at various Strip hotels are (while priced out the roof) a nice way of passing time ogling how the other half buys....
For something besides shows and gambling, you can rent a car and head out west of town to see some pretty scenery at Red Rock Canyon, and if they're still doing it, you can see an old-timey play in the evening. Take a picnic dinner, some nice wine, and a blanket for sitting....
Depending on time of year and your interests, the PBR and NFR have some pretty good rodeo action at either the Thomas & Mack or another hotel arena or so (the Excalibur also has The Spanish Riding School performances sometimes). The Budweiser Clydesdales put on a helluva show when they're there (usually Helldorado which is May, but I think maybe they hit LV downtown during County Fair season too). If college sports is your thing, you can catch the Rebels football or basketball.
And don't forget Hoover Dam as has already been mentioned! As well, unless things have changed (and they may have - I haven't been back since 1994 EXCEPT to eat and shop!), you can schedule a trip to the public parts of the Nevada Test Site for a look at the government's test initiatives since the mid-50s (in which several of my family were involved over many years, beginning with my dad at Enewitok Atoll in 1957, and ending with my brother in and out of the Site to this day).
And that's probably more stuff of less value than any of you really wanted to know....