@Earthmom -Harpers Ferry National Historic Park.
It's very small, not well known, lots of history, tons of hikes (even right along the Appalacian Trail), and you can float or raft right down through it on the Potomac River!
I haven't been there yet, but Congaree National Park is at the top of my list to visit next. It's a less-well-known park but it features a really magnificent old-growth forested wetland. In the spring, it's one of hte cfew places you can view synchronous fireflies!!
In 2016, we took a month-long camping trip and visited 12 national parks. King’s Canyon was (by far) the least crowded and ended up being one of our very favorites for that reason.
I am working on my NP bucket list. I have 22 of the 58 remaining to visit/hike. Glacier has been the most stunning so far, and wildlife sitings are almost guaranteed! They all have something special to offer. The Great Smoky Mountians are my favorite for year round hiking/camping (have visited GSM more than 30 times).
My trick to avoiding crowed trails is to do sunrise or sunset hikes. Many times I begin my hikes between 2-4AM. I am on a peak before sunrise and back down before most are beginning their hikes. Plus you get the bonus of the sunrise!!
I try to avoid weekends on popular trials.
Any park in Utah. Zion is crowded, but still amazing, especially if you get off the main trails and head into the canyons or backcountry trails. I love Capital Reef - especially less crowded trails and canyons.
I like the North Cascades. Even though it is so close to Seattle, you can still find a lot of solitude. I think this must be because it isn't much of a drive-through sort of destination; you have to get out of the car and hike in order to see it at its best.
We are taking an old fashion trip to Glacier National Park this summer by Amtrak from Sacramento to East Glacier, then to Chicago. Only there for 3 days and staying at the Swiftcurrent Historical Cabins to view wildlife on the mountains. Should see mountain goats, big horn sheep and hopefully grizzly. Amazing hiking trails especially Grinnell Glacier. When Sperry Chalet gets rebuilt after last years wildfire, that will be another great hike, hopefully next year. It is common to see wildlife wondering the campgrounds and parking lot. They live there. Don't miss the huckelberry ice cream, pie, or milk shakes.
I just visited the Wright Brother's National Memorial last week while on vacation and it's well worth the stop and $10 admission fee. So much local history to learn about and they even have life-size replicas and a small airport on site. Definitely worth checking out in the Outer Banks!
@Earthmom, I'm not a fan of crowds either! Here are a few of my favorites.