Camping in Hawaii, with a few exceptions, is not exactly a wilderness experience, especially if you fantasize a pseudo-little grass shack on the beach. But it's definitely the choice for those on a budget—even though airline fees for checked bags (tents) have altered the math a bit.
Beach campgrounds are mostly run by the county (each island is its own county) and are usually closed for a day a week (varying, depending on the park) for maintenance and to keep everybody moving. Bringing a larger, walk-in dome tent has advantages, lending a degree of privacy, a larger place to put your stuff and change, etc., and a nice dry pocket in case of rain or strong wind.
On Kauai, Anini Beach is a good bet for visitors. On Maui, Waianapanapa State Park near Hana is sweet, but isolated from the best beaches on the west and south coasts. Oahu's Malaekahana State Recreation Area on the north Windward coast has room to roam. On the Big Island, little known Kapa'a Beach Park in Kohala has some choice spots.
Each Trailblazer guide has a rundown on campgrounds—as well as rustic accommodations and cabins, which are a good alternative for budget travelers. A summary is also included in
No Worries Hawaii, an all-island planning guide.