I wonder what parks you are talking about here? National parks? National forests? Wilderness areas? Habitat areas? BLM land? There is a lot of land, especially out here in the west that is owned and managed by the tax payer. The federal government does a terrible job of managing it, but you can bet huge parcels would go up for sale under a Paul administration.
Much of the land has little commercial value, aside from timber, mineral resources, and recreation. There is still much gold here where I live, some estimates say around 80% of the gold, silver and copper are still lying underneath the mountains most of it on state and national forest lands. It remains to be seen how this land would be managed but property rights would protect a lot of it once it past into private hands because getting gold and other metals out of the earth is a destructive and polluting process. The state or private conservation organizations could spearhead a lot of that. The nature conservancy is one organization that already does that here locally and is very effective at it, more so than the forest service which is a huge overblown bureaucratic organization that mismanages most of the land within the national forest system and has little local connection or concern for it. It could be argued that private land trusts, conservancies, and easement alliances would do a far better job at managing these areas for recreational, resource and environmental uses.
As far as the national parks system, this too would be better managed privately as if you have ever been to a lot of these places they are abused and degrade yearly from overuse. The government finds itself in a unique place in trying to deal with these parks because it being federally owned means they are limited in the restrictions they can place on them and they are required to make the space available for taxpayer use. Yosemite is a prime example or Yellowstone, these would be better contained and managed environmentally by a conservancy that could limit their overall use and abuse. A job the federal government fails miserably at.
). 
