Check the website for the town of Cary for Cary specific information. Classes, free town events, local information.
https://www.carync.gov/
Cary downtown park has a fantastic playground for children and a nice dog park as well. Worth a look.
Raleigh has its own park, Dorothea Dix Park with a lot of things for kids and adults. They have a sunflower field that should be perfect to visit right about now.
There are many good restaurants in the area — local specialty ones and chains. The city of Durham has some great places as does Chapel Hill. Raleigh has plenty but the places are also quite spread out from the downtown area to many other social districts.
There is an area (North Hills) not far from Duke Raleigh that has some really nice restaurants.
Cary also has some nice restaurants — check out Fenton at Cary.
Nextdoor, or immediate neighbors are the best bet to find landscaping firms if the realtor doesn’t have any suggestions.
Hope this helps.