We went through Buffalo River Float Service and rented float equipment. We then camped riverside wherever it looked like a good spot. A lot of the river you can camp riverside since it is a national park.
There are several nice campgrounds but they don't all have floating because they are part of the national park system. There are other great float trip operations that do that for you. Tyler bend is a great area to camp or steel Creek. If you want both you can go to Gilbert https://www.gilbertstore.com/camping-lodging
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