The State Marina at Keehi was/is being rebuilt as a result of Federal Money from the damage caused by the Japanese Earthquake Tsunami. Last year, the waiting list was quite short. Not a free anchorage, however.
As Tasman Cxer suggested, the moorings in Keehi Lagoon would be your best bet for cheap
, though not free live aboard moorings.
Bay in Hilo is strictly short term, seem to remember limited to 21 days. It's PITA to moor there as it's inside the commercial
harbor in Hilo and subject to all the Security
arrangements that go with it. Had to be escorted in and out by a guard and could not have other than crew on the boat. Forget about that harbor though it's a quiet place to hang out to explore Hilo and the Volcano.
Hawaii has no natural harbors. When Captain
Cook visited, the open roadsted at Kealekukua Bay was the safest place to anchor
. All the harbors are man made and tightly controlled. You can anchor off the Kaanapali Coast on Maui but there are probably issues with the State and with the land owners stowing your dinghy
if you hang out too long. That coast and the Kona side of the Big Island are your best bet for a long term anchorage but can be untenable with a south swell and the winter waves.
The State Harbors allow a 3 month stay, space permitting, in any Calendar year. There are usually a couple of boats in Honokohau over the winter getting their three months in October, November, and December and the next years three months in January, February, and March. Once again not a free anchorage, however. By doing that, you can hang out year around but you'll have to move around if you can find space in the various State Harbors.
For the most part, you can anchor out other than the winter months along the leeward coasts or those sheltered from the NW waves. Hanalei Bay is a good Summer anchorage but understand that the State limits length of stay there.
So to sum it all up, NO, you won't find a hospitable anchorage in the islands for a long term stay.