You can take kids into the casinos, but you can't stop and play. There are lots of good restaurants and things to try.
It wouldn't be a new dish, but try In-n-Out burger. It is on the North side of Tropicana, on the West side of the highway. It is the default southwest (formerly California) hamburger and fries. It won't break the bank in case you lose too much money.
Eat at the buffets at breakfast or lunch. Then you won't feel hungry for the rest of the day. The MGM grand should have some lions on display on the main floor. The Bellagio, Wynn and Venetian are fun to walk around and look at. It costs $10 per person to ride to the top of the Stratosphere unless you stay there. Even though you don't need a hotel, I would highly recommend that one if you want a cheap place to stay (and have a rental car to drive to the strip and everywhere else around town).
I gave myself the self-guided tour (basically there is a crater, there is another crater, that is the road to nowhere...) when I was working there last summer (and they don't have any tours planned in December), but seeing the nuclear test sites is interesting, well maybe not to an 11 year old.
http://www.nv.doe.gov/nts/tours.htm
One thing that would be a good idea to go see is the Freemont street light show. It lasts about 8 minutes and starts at the top of the hour (get a schedule on-line or when you get there). Make sure you time it right, as there isn't very much free parking unless you get it validated, and it is a long wait between shows with not a whole lot of kid friendly things to do.