If you have never seen a Cirque show before- Mystere or Love would be great. I think Mystere has the most WOW moments and Love is fantastic in every way. I have also seen O-it was fine but I didn't think it was as good as the other two. I didn't like Ka at all. The stage was great but that was it for me. Jersey Boys is also an excellent show.
To me the must sees would be: the Bellagio fountains and conservatory(at night); Eiffel Tower; Venetain canals and ceilings; Mirage volcano and the Forum Shops at Caesars Palace (both an attraction and a mall). Big Elvis puts on a great free show 3 times a day M-F at Bill's.
Just popping in and out of the various casinos will take good bit of your time since almost every one of them is different.
www.vegas.com/attractions
It is almost impossible to recommend a restaurant without knowing the kinds of food you like, the kind of restaurant you are looking for (casual, romantic, etc.) but most of all- your budget. There are hundreds and hundreds of restaurants in Vegas from inexpensive to very expensive. You should go to one- and only one- buffet (Wynn is good) because it is the "Vegas" thing to do.
Harrah's Carnaval Court is always fun at night. If you don't like what you hear- just take a few steps into the casino and you will be at the Dueling Pianos- also a fun spot.
It would help if you told us how long you will be staying. If it is only a very shosrt trip I would not recommend leaving the strip. If it is longer- you could spend one evening/night downtown.