http://www.handgunlaw.us/
Check it out. There is NO reciprocity in IL, NY or CA.
That said, a bodyguard with a CA permit, is not recognized in IL or NY and is not recognized much of anywhere else. NY doesn't recognize CA. Neither will honor out-of-state or non-resident issued permits.
For example, I live in IN. I can get a FL & TX permit by mail with some classes, fingerprints, etc. But MI will only recognize my IN permit because they will not recognize non-resident issued permit.
I own and carry concealed and I sometimes travel across state lines. It's good to keep current on the laws.
Your I was just giving a general answer, did not want to do all the typing to get to specific.