Each county in Hawaii has its own regulations (or lack thereof) for zoning and permitting of vacation rentals. Please see the links below to get the most accurate information from each of the counties.
It may be of use to you to visit the planning department and planning commission web pages on each island on a regular basis to keep up to date with potential new rules and regulations that are in the works.
A summary of all ordinances on all islands is now available on the website of the Hawaii State Department of Commerce and Consumer Affairs. See http://cca.hawaii.gov/ins?s=Transient+Vacation+Rentals&type=usa for updated information posted on the department's website.
You may also wish to view this general brochure from the state entitled Information for Owners of Rental Property (MAR 2014) (current as of April 2016).
Please note that property taxes will be significantly different for different kinds of properties. For example, apartments and residential houses have different rate structures. If you currently reside full-time on your property and claim a homeowner's exemption, but are considering occasionally renting out a room or the whole property, you may lose your homeowner's exemption which would most likely significantly raise your property taxes. Property tax rates and a summary of ordinances for all the islands are (the last time we looked) for 201/2018 are listed on the following website.
Hawaii (Big Island)
At the time of this page creation, the Big Island appears to have very limited regulations regarding vacation rentals on its books. According to the website (buried under Housing and then "Vacation Directory"), "Apartments, condominiums and homes are eligible to operate as short-term rentals if they are located in areas zoned for such use and/or they have obtained the required authorization(s) from the State of Hawaii and/or the relevant County. It is recommended that before booking a property, you confirm with the owner or manager that the property is operating in compliance with all applicable laws." It does not specify what the applicable laws for the Big Island of Hawaii are or who to check with. If you have or are planning to have a vacation rental on this island it is recommended you check back often to the county's website, pay attention to the Planning Department's postings, and probably visit the county offices in person to stay compliant.
Kauai has a permitting process in place and quite a bit of information on their website that is relatively easy to find. Start with this link.
Maui's website is a little difficult to navigate through. On their home page below is a little box on the left hand side with a binoculars picture. This is where you can input your searches. Start here with the website and then input "Transient Vacation Rentals" into the search box choosing "What is a Transient Vacation Rental?" You will find definitions and answers to frequently asked questions.
See this link for Homes compared to condos: http://www.co.maui.hi.us/1874/Short-Term-Rental-Home-STRH-Application
Oahu (City and County of Honolulu)
The website of the City and County of Honolulu, under the Department of Planning and Permitting has information about Transient Vacation Rentals. According to the section under frequently asked questions, transient vacations rentals have been prohibited outside of resort zones since 1986. If you are planning to operate a new TVR, you should visit the county's web pages and must do your due diligence. See the following webpage and then visit the links under Transient Vacation Units and Bed and Breakfast Homes.