A selection of Shetland lamb fleece in all the natural colors, knitting needles in a size 6, double-row combs and a knife. You could make drop spindles in various weights with the knife, and also use it to cut the yarn. Think of all the spinning variations you could try, and all the knitting patterns you could 'unvent'!
I would also prefer a temperate desert island, if there is such a thing - temperatures in the daytime mid-70's and balmy breezes, with nights cool enough that a wool shawl feels cozy!
Just so you don't have to be quite so darn resourceful, you could move to southern/central California: you'd have the climate you described AND a lot of abundantly stocked LYSs nearby and spinning and weaving suppliers too.