Its been my experience that "primitive" camping with the wife has always been a strain on the marriage lol. If she wants a decently clean bathroom and a shower a cabin might not be a bad idea.
Beavers Bend and lower mountain fork around Broken Bow is pretty, and grat canoe trip. Kiamichi just west is nice also.
N.W Arkansasis really pretty around Beaver lake, White River, and The Buffallo River. If your into canoeing the Buffallo and the bluffs are the ticket. Very beautiful.
Disclaimer: Canoeing is alot of fun, but have seen a few marriages almost on the rocks after a long trip. Have also seen couples that have worked together down river and were stronger for it. Just plan on having fun with it.
I've got a suggestion for a place in Missouri that I've been going to since I was 10 years old. It's called Onondaga Cave State Park and it's in Leasburg, Missouri. It's on I-44 and about 70 miles or so before St Louis city limits. It'd take you about 5 hours to drive there, but it's absolutely worth it. It's not that I'm biased towards it because of the nostalgia of revisiting my childhood campground, but it really is a very nice park with all the amenities you need. Hot showers, flushing toilets, laundry room, and they're all kept as clean as the park, which is immaculate. They have more than enough hiking trails, a clean river to splash/float in (Meremec River), they have 2 cave tours, weekend nature programs at an outdoor ampitheatre, and one thing I noticed after my recent stay there last week, no light pollution! It's been a long time since I've seen that many stars.
Here's a drive-through of their campground that I took:
While Petite Jean is a little outside that 3 hour window if you are not driving crazy, it is a nice area. Morrilton can be used to buy your groceries so you do not have to cart them all the way there. There was a nice restaurant that had a nice view of an overlook. A couple of ponds/lakes to swim or fish. Not sure of hiking trails though. I think you can get campsites with electricity and water for a few more dollars.
A park just a little closer to you is Mt. Nebo. It is positioned on a cliff that used to be frequented by hanggliders. I haven't been there in awhile so they could still use it as the cliff was an awesome launch point to land in the fields below. There are numerous trails, a few used to be along the cliffs. Very nice view and there used to be an antique car museum very close. I am not sure if the campsites are available with water and electric. You can get all groceries at Russellville or resupply as needed.
Devil's Den has already been recommended but is definitely worth checking out. Plenty of trails to hike, can do some caving, depending on rain there are a few waterfalls along the trails, two main ponds to fish, creeks to swim in, and a restaurant and pool that are open certain times of the year. I have camped here lots and never had a bad experience. You can get a campsite with water and electricity for a few more dollars. Not really a big town with anything worthwhile too close. I think the closest is West Fork.
Lake Ouachita will definitely be outside the 2-3 hours but there is plenty of things and places to see. If your wife wants to get a little pampering, you can always take her to a spa day in Hot Springs. Not sure about the trails but Lake Ouachita does have some very nice striper fishing if you two are interested.
Those are a few of the places that are in your driving area in Arkansas. Used to frequent quite a few of them when I lived there. For Oklahoma, I have enjoyed Roman Nose and Red Rock Canyon. Roman Nose has two ponds/lakes to fish and several trails. Red Rock has a nice canyon experience with trails and a very small pond. I do believe both Red Rock and Roman Nose have water and electricity in some campsites.
I will suggest Robber's Cave, 2 hours south of Tulsa. Cabins down to primitive campsites. Showers and flush toilets available. Swimming lake and 2 fishing lakes, hiking trails, rock climbing up to and around the cave. it is an old park but is well maintained (at least it was 2 yrs ago). That was the first time I got my wife to sleep in a tent, she now is not opposed to tent camping.
I would suggest Tahlequah. My wife and I camped there last weekend. You have two choices. You can camp out by the river or down by the lake. I prefer the river at this time of the year as running water is a lot cooler than lake water. We had a blast last weekend with about 4 other couples and we all camped. We couldn't do an open fire due to the burn ban, but we were allowed a charcoal grill which was good enough.