My favorite type of outing! I've included some places that are great for a nature lover, but don’t necessarily have nature centers.
Hidden Oaks Nature Center – small but nice programs (Annandale, VA)
Brookside Gardens - (Wheaton, MD)
Huntley Meadows (Alexandria, VA)
Meadowlark Botanical Gardens - has an entry fee (Vienna, VA)
Occoquan Regional Park - let's you rent canoes/kayaks (Lorton, VA)
Pohick Bay Reginal Park - also lets you rent canoes/kayaks (Lorton, VA)
Keniworth Aquatic Gardens - best when flowers are in bloom (Washington, DC)
Mason Neck State Park (Lorton, VA)
Prince William Forest Park
Calvert Cliffs State Park – hunt for fossils and hike, but this place is a little bit of a farther drive
As something different to do - I love getting out on the water for a quiet paddle. Totally different way to observe nature. I call it hiking with my arms .
The post had an article on gardens to visit -
http://www.washingtonpost.com/gog/best-bets/best-gardens,102153.html?hpid=z13
Some of them may appeal to your kids – not all are formal gardens.
Many of those parks also have tours or activities that may appeal to your kids.