Cary has dozens of really great parks. The Town of Cary has a great parks section to their website - just pull that up and see what's closest to your hotel. There are pictures and amenities listed.
This is the suburbs, most everything is family friendly.
I will warn you about this - Cary and most of the surrounding areas have *very strict* building codes in regards to signs and buffer landscaping around businesses. I love this - no glaring neon flash everywhere - but man when you are trying to find things it can be a pain in the tukus. You can drive down streets past all sorts of things AND NOT SEE THEM.
So do a little planning, just driving about can be less than productive unless you really like looking at trees and shrubs
You will likely have a hard time getting a realtor to spend that much time with you when you aren't buying for almost a year. I'd map yourself out something in whatever realtor site you like and GPS tour yourself.
Good luck, and it's still in the 90's here. Dress cool.