So if going to the store we aren't allowed to store the gun in the car because it's private property? But if it's a sensitive place we're allowed to store it in our vehicle?
There are a lot of conditions depending on the circumstances. Also parts of sb1230 are currently stayed in federal court, in particular the private property approval requirement.
1. Carry license or no carry license.
Sensitive places and private property w/o approval only applies to those with carry licenses and the licenses firearms. If you do not have a carry license then those do not apply to you. Instead you still follow place to keep (restricted to home, range, place of employment, etc).
2. Entire Private Property: If you have a carry license and there is no "guns allowed" sign, then the licensed gun would have to be off the private property, even if stored in a car. This is due to it affecting the whole property to include the parking lot, unless otherwise specified.
3. If you have a carry license and going to a private property(w no "guns allowed" sign) that is also a sensitive place, then #2 still applies and can't have your licenses gun in the car unless otherwise specified.
There was talk on enforcement at shopping malls with some stores allowing guns and others not. I believe you can carry or store firearm in the car on the mall property in that case.
Other county laws may change things in Honolulu, who's private property signage requirement is technically still in effect, and Hawaii County.