Do I need to report my new address within 24 hours to immigration when I move to another city in Thailand on a retirement visa?

Well, if that's where you're going to live, you or your landlord need to go to that immigration office and file a TM 30 (notification of Foreigner in residence), and while you're there you need to ask them if that office also requires a TM 28 (change of address).

Once you get those filed you should be able to do your 90-day reporting and your subsequent extensions at that office.