The most important thing to do is find all four parts of Captain Lawrence's journal, plus the two pieces of paper that give directions in the ice caves.
Where do I find all the journal parts?
When you've got those papers, keep going down your task list. When you've done everything you can, look for a time when you come into town and find the place deserted.
When that happens, it may be time to head for the ice caves.
How do I follow the directions in the caves?