I just responded with a list of inexpensive things to do in Vegas, but it is gone. I will quickly try to list them again for you.
Station Casinos are local hotels off the strip with family fun. You can put your child in kid quest while the two of you have a little fun. Call them for details because I know you will need the immunization record.
You may want to get their players card for the discounts.
I will stop here and edit to be sure this one sticks!!!!
http://parks.nv.gov/
http://www.birdandhike.com/Bird/Red_Rocks/Calico_Basin/_C...
Mount Charleston, Red Rock Canyon, Spring Mountain Ranch, & Calico Basin, are all cooler, off the strip, places to hike, enjoy the scenery, and have a nice lunch. Some small fees may apply.
Bonnie Springs is also in the area and very inexpensive and for the most part free. Ghost town and small petting zoo with horse back riding option.
http://www.jrponyparties.com/
JR Pony Farm is a small farm that many of the kids have birthday parties at. They also have pony riding days and camp days. If it is a camp day, there are a couple of hotels within a couple of miles where you can watch movies, eat, gamble, and maybe bowl.
Ice Skating at Las Vegas Ice Center or the Fiesta hotel.
The links below are off the strip, fun, inexpensive, and sometimes cooler.
Enjoy!!
http://www.nationalatomictestingmuseum.org/
http://www.nvoutdoorkids.org/
http://www.usbr.gov/lc/hooverdam/
http://www.nps.gov/lake/index.htm
http://www.vegas.com/attractions/off-the-strip/clark-coun...
http://www.clarkcountynv.gov/parks