Over the last century SCOTUS has been selectively 'incorporating' the Bill of Rights to apply against the States (and hence municipalities formed under those states).
Ripped from Wikipedia:
Right to indictment by a grand jury
This right has been held not to be incorporated against the states. See Hurtado v. California, 110 U.S. 516 (1884).
Protection against double jeopardy
This right has been incorporated against the states. See Benton v. Maryland, 395 U.S. 784 (1969).
Constitutional privilege against self-incrimination
This right has been incorporated against the states. See Malloy v. Hogan, 378 U.S. 1 (1964).
A note about the Miranda warnings: The text of the Fifth Amendment does not require that the police, before interrogating a suspect whom they have in custody, give him or her the now-famous Miranda warnings. Nevertheless, the Court has held that these warnings are a necessary prophylactic device, and thus required by the Fifth Amendment by police who interrogate any criminal suspect in custody, regardless of whether he or she is ultimately prosecuted in state or federal court.
Protection against taking of private property without just compensation
This right has been incorporated against the states. See Chicago, Burlington & Quincy Railroad Co. v. City of Chicago, 166 U.S. 226 (1897).
So in the main the 5th does in the main apply as a restriction on the powers of the City & County of Honolulu.
The McDonald Vs Chicago decision incorporated the 2nd Amendment as a restriction on the powers of the States and the municipalities formed within them.