Could you explain more about the NUC? How does it affect the rental process? How does it affect me, the renter?
All sleeping quarters, including private homes, apartments, condos, bedrooms in homes, campers, tents, etc. on Oahu cannot be legally rented for less than 30 days. There are two exceptions to this law - 1) units built on resort-zoned land and 2) homes with the NUC.
NUC and B&B permits have not been issued since the late 80's and they are extremely rare. If you see a property on AirBnB, you should ask for the physical address and cross-reference with the NUC list above to make sure you are renting a legal unit. If the unit is not listed on the NUC list, you can try checking the zoning on the GIS map
http://honolulugis.org/
Generally, most Waikiki units between Kuhio Ave. and the beach are legal because they are built on resort-zoned land, as are the ones in the Ilikai and Ala Moana hotel. Most units between Kuhio and Ala Wai Blvd. are not legal and cannot be rented. The legal units between Kuhio and Ala Wai Blvd. (such as Waikiki Banyan) have NUC numbers.
Other resort areas include the apartments next to Aulani (but not the residential areas across the main street), Turtle Bay, Kahala hotel area, and Makaha Valley.
Starting soon, short term rentals will be required to publish their TMK (tax map key) and TAT (transient accommodation tax) number in order to be listed on sites like AirBnB. If the unit has a TAT, it is legal and you do not have to check zoning or for a NUC.