that being said...i thought kauai would be best, because there are already some people living primitively (or near it) in Kalalau Valley. it's remote (an 11 mile hike in) with no roads to it, so the police/rangers don't go there often. there are some other posts about kalalau on here if you're interested.
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foget Oahu, too many people.
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never been to Lanai, but most of the island is owned by this billionaire and mostly just expensive hotels on it.
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Molokai has a small population, but its a small island. the only place you could get away with living primitively might be on the north shore, but its pretty remote and hard to get there and also there are some families up in some of those valleys that got pot growin operations goin, and you'd probably get shot and killed if you're found explorin around there.
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Maui might be doable. Forget about the westside, you'll get run out of there. You might be able to do it around Hana...pretty remote out there. There are tons of hikers and people goin out there tho, but perhaps you could go deep enough to find somewhere to not get bothered. i don't know, i haven't spent much time there.
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Ni'ihau and Koolawe you're not even allowed to go on, so thats out of the question.
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On the Big Island - Waipio Valley and that area looks nice, but there are people practically homesteading back there and you WILL get run off. the only other place would be out in the Puna District somewhere, but then again you'll probably get run off by pot growers/local thugs there. you might however be able to hookup with one of the eco-villages there that would be sympathetic to your cause.
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Like I said, you'll want to be near fresh water AND by the ocean. So I'd say Kalalau really is your best bet. And then Hana area in Maui would be second. Remember, you need permits to "legally" camp anywhere so thats why Kalalau would be best - the rangers only go in once or twice a year to check. Otherwise, local fisherman are gonna be pissed your setting up camp in their local fishing spot, or the DLNR/police will see your camp and arrest you, or local thugs are gonna see a bunch of haole hippies on the beach and cause problems for you. Just my two-cents tho!