JC Raulston Arboretum

4415 Beryl Road, Raleigh, NC - (919-515-3132)
Description: botanical garden (partial shade)
Parking: provided
Ages: 0-Adult
Cost: FREE
Hours: open 7 days a week (8am-8pm)
Notes: Another beautiful garden to stroll in with your kiddies. This garden has lots of interesting plants, a Koi pond and a big shady lawn to run around in. Most areas are stroller friendly. Open all year round. Part of the NC State Campus.
Website: http://www.ncsu.edu/jcraulstonarboretum/visit/visit.html

Hemlock Bluffs

2616 Kildaire Farm Rd, Cary, NC  - (919-387-5980)
Description: Nature center & trails (shaded)
Parking: provided
Ages: 0-Adult
Cost: FREE
Hours: sunrise to sunset
Notes: Beautiful park, but heads up, lots of stairs. This is not a stroller friendly walk. Also, bring your mosquito repellant. Sometimes you can hear music from the Koka Booth Amphitheater down the road.

Website: http://www.townofcary.org/recreation-enjoyment/parks-greenways-environment/parks/stevens-nature-center-at-hemlock-bluffs-nature-preserve

Fearrington Village

2000 Fearrington Village Center, Pittsboro NC - (919-542-2121)
Description: shops, restaurants, garden and farm (full sun)
Parking: on site
Ages: 0-Adult
Cost: FREE
Hours: Tues-Sat (10am-7pm), Sun (10am-4pm) Shops closed Monday.
Notes: Come see the belted goats and cows and stroll through the gardens and shops. Enjoy a treat at The Belted Goat cafe and let the kids explore the grounds. Most areas are stroller friendly. Only one bathroom. It's located in the cafe, but there is no changing table. Open year round. Check the website for seasonal events.
Website: http://www.fearrington.com/village/theshops.asp

Sarah P. Duke Gardens

426 Anderson Street, Durham, NC - (919-684-3698)
Description: botanical garden (partial shade)
Parking: $2 per hour. Bring $1 bills as pay stations don't make change.
Ages: 0-Adult
Cost: FREE
Hours: Mon-Fri (9am-6pm) Sat (9am-5pm), Sun (noon to 5pm)
Notes: This is a beautiful garden, but it is mostly unpaved trail. Some parts are stroller friendly, but you might want to bring a baby sling. Feed the ducks, play on the south lawn or take pictures in the Asiatic Garden. Bring a blanket and have a picnic or eat at the Terrace Cafe. Open all year round. Part of Duke Campus.
Website: http://www.hr.duke.edu/dukegardens/

UNC Botanical Garden

1000 Laurel Hill Road, Chapel Hill, NC - (919-962-0522)
Description: botanical garden (partial shade)
Parking: provided
Ages: 0-Adult
Cost: FREE
Hours: Mon-Fri (8am-5pm) Sat (9am-6pm) Sun (1-6pm)
Notes: Most areas stroller friendly. Spring is the high season.
Website: http://www.ncbg.unc.edu/

Coker Arboretum

East Cameron Avenue, Chapel Hill, NC - (919-962-0522)
Description: botanical garden (full sun)
Parking: on street / metered or pay lots. Free on Sundays. 
Ages: 0-Adult
Cost: FREE
Hours: Sunrise to sunset
Notes: Stroller friendly. Well maintained and beautiful all year round. Spring is the high season.
Website: http://www.ncbg.unc.edu/pages/38/