If you are a hotel guest they have a free airport shuttle...
...Not sure about public transit from the airport to Summerlin, but my guess is it is a huge hassle. There are also shared limosine services such as Belltran that are reasonably inexpensive. A rental car in Vegas is, in most cases, the best as well as least expensive choice if you're planning on casino hopping off-Strip.
The only casino close to the SunCoast is the Rampart, about 3/4 of a mile away, right down the street.
Good luck and enjoy your visit,
Cobbson