What should I do in Vegas?

I’m in Vegas for the first time, and I’d love some advice on what to do (other than drink and party).

In particular:
1 – What should I do during the day? Are there any unusual things to try? Is it worth going outside of the city?
2 – Any restaurant I shoudn’t miss? Anything of the caliber of Alinea or Per Se?
3 – Any favorite shows?

Thanks!

-Nick