McInally Palms is a bit nicer than the previous island - it comes with a warm welcome from the booth worker Ingo, AND a hotel! Oh, and a massive graveyard, but that's a bit grim.
After talking to Ingo, that's up to you!
For a general indicator of progress, you can find two useful items without going inside any buildings.
Like something you'd rub on your hands.
Directly left of Ingo, you get the greasy sunscreen by agreeing to rub it onto the Pale Girl's back.
Have you found something that's too hard for Cleo to move?
On the right side of the island.
Atop the lighthouse, a tight screw is difficult for Cleo to loosen; use the sunscreen on it.
You can find the lemon north-west of Ingo, in a graveyard - cross two bridges and a small lemon tree is atop a grave.
Do you remember reading about lemons anywhere?
Check your Cocktail Bible - it's still in your inventory, and one of the cocktails requires a lemon.
Base: Salt Lick Smitty - Tequila Modifier: Sherbet Powder Flavor: Lemon
Have you thoroughly talked to everyone on the island?
Try heading indoors.
Enter the McInally Hotel, and talk to everyone in the lobby.
Remember that the 'Risky On The Docks' cocktail has a clue in its name.
The hotel guest writing in her travel diary needs to live a little.