On the east side of Ranch Island you'll find a boat dock and rowboat. The rowboat will take you to Lighthouse Island (and Sunny Island after you unlock it). Lighthouse Island is just to the east of Ranch Island.
An old lighthouse use to be on Lighthouse Island. Now it is just ruins of the building's base blocks. There's nothing here on the island, but you can do some fishing off of the dock if you want to.
Hidden Sun Stones
You will find 1 Sun Stone on the island. Go to the back wall of the ruins and press A to find the stone.