The Museum of Life and Science in Durham is an amazing museum with extensive grounds full of fun exploring for kids. Come on a day with good weather because the outdoor area is the best part. Buy tickets with the mini-train ride because it's fun! You go twice around the track, which takes ten minutes, right in the middle of the forest and there are things for kids to spot like animal-shaped hedges or shiny silver fish sculptures. An incredible part of the outdoor area is the Dinosaur Trail. Here there are sculptures of dinosaurs in the middle of the woods, with plaques providing information about the dinosaurs! Their scales look so real and they are gigantic! It is a joy to walk around checking out each one! There is a dusty fossil dig area at the end of the Dinosaur Trail with dirt from a mine in Eastern Carolina that used to be the ocean floor- your kids will find real fossils and can then identify them on the board.

A farmyard area is a cute (and stinky) place to see alpacas, pigs, goats, cows, and rabbits.
A long boardwalk leads you around a wetland to enclosures of bears, wolves, and lemurs, and the Into the Mist exhibit. Don't miss this area! It's a half hour walk around the entire area, plus add time to stop at each exhibit (one and a half hours total is good). There is a water play area on a patio over the wetlands, and buttons kids can press to hear the sounds of animals. At the bear exhibit, sometimes you can't see the bears but you can track them on a screen. You can also see bear and wolf poo!- kids always love potty humor.  The lemurs have a cute exhibit with little houses on poles. They love to swing from house to house. The wolves are interesting to watch, walking slowly along the top of the hill in their forest exhibit. There is a tall yellow contraption where kids can play Catch the Wind. And best of all, Into the Mist! This is an incredible area with remote control sailboats, a hilly spot where cool mist rises up in the tiny valleys, a sunken area with mist, a geometric area with mist, and tunnels under the grass. 
Another amazing part of the outdoor area is the treehouse playground called Hideaway Woods! Wow what a playground! Here a bunch of treehouses connected by rope bridges provide hours of fun! What a blast! There is also a stream lined by rocks with clear water that kids love to play in.
The butterfly  house is a conservatory with pretty, tropical flowers, and some colorful butterflies. There are also pinned (dead) butterflies, and an insectarium with some amusing creatures. I love the blue poison dart frogs here. 
Nearby is the cafeteria, which is very crowded and unpleasant at lunchtime and smells pretty greasy- bring a packed lunch if you can. The cafeteria is not bad around 11:15am though.
Directly behind the museum building is a rope and wood playground called Gateway Park that is a ton of fun.
Inside the museum, there are two-storeys of hands-on science exhibits. These could use a little more explanation on what to do. There's plenty of room to roam and kids enjoy jumping around on the two big square areas where shapes are projected on the ground. There are also air pipes you shoot balls and parachutes up. There are exhibits about shadows, stop-motion film-making, pulleys and pipes, and more. In the middle is an area of tanks filled with fish, screech owls, and reptiles.
In the entry building is a coffee shop inside a gift shop where you can buy many different science sets. It's an attractive shop!
The museum holds special events that cost extra, such as the Pumpkin Patch and Santa Train. In October, you catch the train to the forest where a tent is set up with craft items to decorate a pumpkin that you choose. There is a corn pit and other games, then you ride the train back. In December, the museum is lit up beautifully for the Santa Train. You ride the train to the forest, where Santa greets you, and then you ride it back. There is hot chocolate and crafts. You must buy tickets for the Santa Train on the very morning they come out, around November 1, otherwise it sells out.
A nice place three minutes drive away is Northgate Park, where you can go for a stroll on a wide path. 
12 minutes north, check out West Point on the Eno River, a park with historic mill, tobacco packhouse, farmhouse, tee pee, log play area, and dam like a waterfall.
Another place to check out is Duke Homestead and Tobacco Museum, seven minutes drive west.

Directions

Museum of Life and Science is located at 433 W Murray Ave, Durham, NC 27704.
Open 10-5. Closed Mondays. 
Admission is $20 for adults, $18 for seniors and military, $15 for children, and free for children 2 and under. Train rides are $5 each and $3.50 for members. Parking is free. On Durham community days, residents of Durham with ID enter for free. Membership is $130 a year for two people, and allows 9am entry- this is definitely worth it.

Click on map for interactive view