There are several state, country, National Forest, and private campgrounds in the area, offering primitive to near-glamping facilities. If you're looking for hotels/motels, there are a couple close to the mine, but more options in Hot Springs, if you don't mind a 45 minute drive. Campgrounds fill up fast on summer weekends, so I recommend making a reservation! Edit: As for the heat, it depends... I've seen 60 in June and 80 in February... Definitely prepare for mosquito swarms that can carry you off and ticks... Take shade to the mine with you, because it's wide open with very little shade.
It's beautiful country and there is the Caddo River and a lot of people canoe the river. I'm sure there is camping, just don't know how close to the mine. It will be hot and some spots are open so the sun will be beating down on you. I would be there in the morning.
We went in late April and it was still a bit chilly. Early June should be mild. Can't say on camping, we stayed at an airbnb.
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