The straightforward substitute is South Marco Beach Access, a little under two miles south, where you park on Swallow Avenue and walk across to open Gulf sand. Same water, same sunset, public.
For a beach that feels genuinely different rather than merely accessible, go north to Tigertail Beach Park and cross to the Sand Dollar Island spit. It takes more effort and repays it in space, birds and shells.
If your accommodation is a beachfront resort, you already have a private stretch of sand with rentals and service, and Residents' Beach adds nothing to it.
And if the appeal was the idea of a quiet beach with no crowd, the real answer on Marco is not a beach at all but a boat. An hour's run south puts you on Kice Island or the outer Ten Thousand Islands keys, where the only footprints are the ones you make. Half-day shelling and beach-drop charters run from the marinas at the north end of the island and from Goodland, and for a family of four the cost is not far off a week of beach club fees.