Marco Island has a short indoor list. That is the honest starting point, and any page that presents twenty wet-weather options here is padding. What the island does have is a climate in which most rain is not a lost day, and the useful skill is telling the two kinds apart before you write off the morning.
From roughly May to October the rain arrives as an afternoon convective storm. It builds over the interior through the day, moves west, delivers a violent thirty to sixty minutes with a great deal of lightning, and then the sun comes out and the air smells of wet asphalt. On a summer afternoon the right response is usually to go somewhere with a roof for an hour and then carry on. Boats mostly do not cancel for rain, though they absolutely do cancel for lightning and high wind, so the scheduled morning departures are largely unaffected by this pattern.
From December to March the rain is different and rarer. A cold front comes through, the temperature drops ten or fifteen degrees, the sky goes flat grey and it drizzles on and off for a day, occasionally two. This is the genuine washout, and it is also the version that makes the beach unattractive rather than merely wet. That is the day this page exists for.
What is actually open on the island: a free museum that is better than it needs to be, a free art centre, a cinema at Marco Walk, bowling and arcade games attached to one of the resorts, the library, the shops and restaurants at the Esplanade and the plazas, and the spas at the beachfront hotels. That is close to the complete list, and it is enough for one wet day rather than three.
For a full washout with children, or a second consecutive grey day, the correct answer is the car. Naples is roughly twenty miles north and has museums, a covered shopping district and a children's museum. Rookery Bay's Environmental Learning Center is closer than that, on the mainland side of the causeway, and is a genuinely good indoor hour. Both are below.