MGM and Mandalay have the best pools. Their rates are moderate (MGM is usually cheaper of the two). Excalibur, NYNY, and Circus Circus all have more kid-friendly amenities and tend to be budget-friendly, but I really wouldn't say that they particularly cater to kids and families (and none of the Vegas hotels really do). Some are more family-friendly than others, but none are actively trying to draw families in. I would avoid CC though - it's not that nice of a place,, and it's not really close to anything else. It would be fun to visit.
The best hotel for families IMO is The Orleans. It's a little off the strip and does offer some kid-friendly and family-friendly amenities. There is a shuttle to the strip.