The Amelia Island Museum of History at 233 South Third Street is a good place to start if you want to understand the island's layered past before you go exploring it. The "Eight Flags" concept — the eight different national flags that have flown over the island — organizes the chronology from early Timucuan habitation through French and Spanish colonial periods, British occupation, the oddball episode of the Patriot Army, and eventually American control.
The building itself is worth attention: it was the Nassau County Jail for most of the twentieth century, and the renovation preserved the institutional bones while making the space work as a museum. The guided tours are genuinely good — the docents know the local history in detail and have an opinion about it, which makes for a more interesting visit than a self-guided one. Check the website for tour times.