This page is going to be more honest than most: Amelia Island is not a good rainy-day destination. It has one small museum, eight blocks of shops, and almost nothing else under a roof.
Knowing that in advance is worth more than a padded list, because it changes what you do with the day.
First, work out which kind of rain it is
A summer afternoon thunderstorm is not a rainy day. From June through September these arrive most afternoons, last under an hour, and clear. The correct response is lunch, a shop, or a bar, and then back out. Do not rearrange the day around one.
A frontal system in winter or spring is a genuinely wet day — grey, steady, all day. That is the one this page is about.
What genuinely works on the island
The Amelia Island Museum of History. Small, well done, housed in the former county jail, and the fastest way to understand the Eight Flags story and the railroad and shrimping history that built downtown. An hour or two, and it is the single best indoor option on the island.
Centre Street. Eight blocks of independent shops in Victorian storefronts, plus the cross streets. In the rain the awnings and the tight block pattern make browsing viable in a way a retail park never is. Check hours — these are independents, so late-morning openings and early closes are the norm.
A long lunch. Downtown has the density to make this a plan rather than a consolation. The courtyard restaurants have covered seating; the bars have the atmosphere for an afternoon that is not going anywhere.
Resort facilities, if you are staying at one. Indoor pools, spas, fitness centres and children's programming are the reason a resort holds up in bad weather better than a rental does.
The Palace Saloon, if only for the room. Florida's claim to the oldest continuously operating bar is exactly the sort of place a wet afternoon is for.
What does not work
The beach, obviously — though a walk on an empty grey beach in a raincoat is genuinely good and almost nobody does it.
The Egans Creek Greenway floods in sections and the trails hold standing water.
Fort Clinch is a masonry fort with ramparts and a parade ground. There are covered galleries, but it is fundamentally an outdoor visit.
The lighthouse cannot be climbed on demand in any weather.
Kayaking. Guided trips will be cancelled, and rightly — a marsh with no shade is a bad place to be in a thunderstorm.
The right answer: drive to Jacksonville
Forty minutes south is a city of a million people with everything an island of thirteen thousand does not have: museums, a zoo and gardens, aquarium-scale attractions, cinemas, a proper mall, and indoor everything.
If the forecast is wet all day, this is not a fallback — it is the plan. Leave in the morning, come back for dinner downtown.
The half-measure worth knowing
Kingsley Plantation and the Timucuan Preserve visitor facilities are on the way south, roughly twenty-five minutes away, and combine a short outdoor visit with indoor interpretation. In light rain that works; in heavy rain keep driving.
Plan for it in advance
If you are visiting between December and March, or in high summer, assume you will lose one afternoon to weather and hold something for it — the museum, or the Jacksonville drive. The mistake is spending a wet day driving the length of the island discovering that things are outdoors.