Looking to tent camp in northeast Arkansas...

Hard to beat the White River/Crooked Creek/Buffalo River/Bull Shoals/Norfork Lake area around and close to Mountain Home, AR.
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Fully Agree.

I would definitely recommend looking at anything along the White or Buffalo River. Bull Shoals is also a great lake/area.

Is there a specific spot/campground along the white or buffalo that you would recommend? Lots of mountains?

Depending on the type of camping you want to do:

If you are looking for some 'real' tent camping I would strongly suggest renting canoes and going down the Buffalo River and camping along the sand bars at night. You can rent canoes in any city near the river, they will drop you off and pick you up and they have spots for you to park. You can do anything from 2 hours up to several weeks. I would call around and price the rentals and also ask them to suggest a route. Most everyone is very nice and should be able to help out. (just google Buffalo River Canoe Rentals)

If you are looking to camp and still have some amenities for the family like showers, restrooms, access to stores then I would suggest:

Bull Shoals State Park
29 Bull Shoals park
Lakeview, AR 72642
(870) 445-3629

Bull Shoals park is on the white river right below the damn to Bull Shoals lake. This is a great park...lots of things to do. White River is amazing with crystal clear, cold water year round surrounded by smaller mountains. Right above the park is Bull Shoals lake which is also amazing. You can rent boats, hike, camp, etc...and you will also have access to stores, bathrooms, showers, etc...

The state parks are great in Arkansas so I would suggest cruising through the list AR State Parks