This museum is small. There are some interesting exhibits, especially if you like nautical things, boats, and historical facts. But it is not incredibly kid-friendly, and none of the exhibits are really interactive. If your child can't read and does not stay still for very long or does not enjoy small, crowded spaces, they will probably drive you crazy and make you want to leave fairly quickly. This was our experience with a two-year-old.
Admission is "free", but a donation is suggested, actually, more like expected.
If you go, don't expect to spend more than an hour here.

This little-known blueberry farm is a great summer activity. Blueberries cost $2 per pound, and are available all summer, from beginning of June until late August or beginning of September. Buckets for picking and take-home bags are provided free of charge. There is also a small play area with swings, a slide, and a sandbox.
Great fun for kids, parents, and grandparents.
Don't forget to wear sunscreen and bug spray.
Warning: there are no public restrooms.

The playground has recently been revamped with brand-new, modern equipment and it is so much fun! Definitely worth spending a few hours or an afternoon. The park's original structures include swings, a small slide, see-saws, and a large picnic area with a fireplace. There are ample picnic tables, and water fountains for thirsty people. There is also a path that goes around the perimeter of the park, but it is currently being updated, and might not be completely accessible. There are also no public restrooms at this park (which is why I give it 4 out of 5 stars).

For canine lovers, there is Northgate Dog Park, located across the street from the playground. It has a section for smaller dogs and a large fenced-in area for larger dogs and their playmates.

Little known fact: If you walk past the dog park and continue down the paved path, you will end up on Murray Ave., next to the Museum of Life and Science picnic area, where the old Dinosaur Trail was once located.

Whether you are in Durham for a day, a week, or a year, you have got to visit Duke Gardens. This is the place when we take all out-of-town guests. There is no "bad" time to go: it is always fun and beautiful there! It is an amazing wealth of horticulture, and is ever-growing and changing. There are ample walking trails, and opportunities to feed the wildlife, which is always very popular with children. This is one of the most popular bridal/wedding photography sites in the Raleigh-Durham area.
Admission is free for everyone. Parking normally costs $2 per hour, but it is free on weekends before 1pm.

Duke Park has something for everyone. Trees to climb, hills to run up and down, a giant field to run in and play tag, plenty of baby swings, and the biggest slides we have yet to find in the Triangle area!
As a mom and childcare provider, I also appreciate that the play area is open and that it is easy to see everything in the playground, even when you have multiple kids running around and doing different activities.
There are some play structures geared just for younger kids, like small yellow and green slides, a red tube to climb through, and a little pretend house. Then there are things older children will enjoy, like a climbing wall, a really cool rockin' teeter-totter, a disc-shaped swing that twirls around, and of course, the humongous slides.
They even have a little wooden fort to play in, additional swings, and some old-school style teeter-totters for little ones, located off to the side of the main play area.
There is also a nicely paved path that meanders around the park. Great for strollers, trikes and bikes. Also fun for drawing with chalk.
The reason I am giving it four stars instead of five is that there are only two benches for parents to sit on, and the play equipment is not nearly shaded enough, so it gets hot very quickly.
Also, there are no public restrooms at Duke Park. I don't mind having toddlers pee behind a tree every now and then, but it is fairly inconvenient, so try to plan accordingly.