Have you considered Charlotte, NC or nearby suburb? LOTS of family friendly and outdoor stuff to do in Charlotte and the surrounding suburbs because they are also big. Moving away from Charlotte due to job transfer but going to miss everything there is for kiddos/families to do here! I use to hate this place with a passion (you can see in my old posts, but now that I am leaving I am sad and going to miss it. I think I thought the grass was going to be greener in the Raleigh area, and then I realized the areas in which I am looking are rapidly growing tract house suburbs but without the amenities of Charlotte, or so it seems to me right now. I hope to be pleasantly surprised when we get better established there
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I can probably think of 100 things off the top of my head lol, but I won't list them all as that would take all day and then some! Just to name a few:
All of these are in Charlotte or an hour or less away, depending on what part of Charlotte one is in:
US National Whitewater Center (ziplining, hiking, mountain biking, rafting, kayaking, all sorts of festivals and concerts throughout the year). Fun to just go and grab a bite to eat and watch people raft. Toddler enjoyed climbing on the big rocks, running up and down slopes.
Imaginon Children's Library
Discovery Place Science Museum
Discovery Place Nature Museum
Discovery Place Kids in Huntersville
Mint Museum (various locations, with specific activities for kids and kids adults)
Nascar Museum (I'm told they have kids stuff)
Wells Fargo Museum (never been, but I'm told they have kids stuff)
Various Art Museums (haven't been, forget the names)
Variety of JumpZone/Bouncy House establishments and Gymnastic Centers
Daniel Stowe Botanical Garden in Belmont
Winghaven Gardens
McDowell Nature Preserve and Nature Center (offers a ton of kids activities and family activities, i.e. family kayaking tours, etc)
UNCC Botanical Gardens
Franke Liske Park (traditional park + paddleboating, putt putt, etc)
Freedom Park
Ray's Splash Planet (indoor, year round water park and fitness center)
SeaLife Aquarium at Concord Mills Mall
Great Wolf Lodge (indoor water park and hotel)
Lots of splash pads and greenspaces uptown (too many to list)
Crowder's Mountain in Gastonia
King's Mountain National Military Park
Schiele Science Museum in Gastonia
Cherry Road Park in Rock Hill, SC
Glencairn Gardens, Rock Hill, SC
James K. Polk Historic Site in Pineville
Main Street Children's Museum in Rock Hill, SC
York County Museum in Rock Hill, SC
Various greenways, ie McMullen Creek, McAlpine Creek, Little Sugar Creek, etc
Lake Wylie
Lake Norman
Spencer Transportation Museum
Tiger World
Lazy 5 Ranch
Various malls around here have indoor and outdoor kids play areas (i.e. Pirate themed at South Park Mall)
Ice Skating Rink in Pineville
Charlotte Douglas is a major airport with a space dedicated for picnicing, walking, or watching planes take off.
There are so many library branches and each one I have ever been to has great activities
The Energy Explorium at McGuire Nuclear Plant (Shearon Harris has one, too, but haven't been to it)
Carowinds Amusement Park
We can be on the Blue Ridge Parkway in about 2 hours, so we have done a lot of day trips to Boone, Blowing Rock, or play in the creek at Julian Price Park and hike various trails on the parkway.
Asheville hiking and Biltmore house are about 2.5 hrs away, so just a little farther than I personally would do a day trip, but could be done by older kids I think.
Charleston, SC is about 3-3.5 hours away. We like Folly Beach because the parking is free.
Riverbanks zoo in Columbia, SC is about 1.5 hrs away from us, so great for day trips. We like it better than the Asheboro zoo, as it is less spread out and therefore better for little kids in my opinion. They have botanical gardens, water park, playgrounds, rides, in additional to the usual zoo stuff.
Oh, and I guess if you care about football (we don't lol), there is always something going on with the Panthers it seems.
Public schools here get a bad reputation, therefore there are a lot of private options.
These activities were just off the top of my head quickly! There are so many more!
This post started out to help the OP whose affinity for outdoor family activities seemed to echo my own family's interests, but now I think I got carried away mourning the loss of some of my favorite things to do lol. Good luck with your decision. Maybe you just need to consider some different parts of NC?
I will say that as I have asked for family-friendly things to do in the Raleigh area, various people have only given me the same few answers: Marbles Museum downtown, Museum of Life and Science in Durham, and "the parks." I do look forward to exploring, as I am sure there is more to do than that...maybe make a post asking for that and see what you get? Also people often suggest organized sports, but part of the reason I prefer the activities I listed is because they do not require signing your kid up for something while you sit on your butt on the sidelines and watch or don't watch because you are on your smartphone. That is exactly what some people want, but not us.