"Light and mellow wines suit the sunny lands where the grapes grow, but here in the North, it needs something short and more potent to keep the cold from a man and restore his vitality". Isle, Ben and Loch, from the Clyde to Skye. S Heckstall Smith, Edward Arnold, London, 1932.
Some distilleries are in really lovely buildings like Ardbeg, Bruichladdich and Lagavulin which are definitely worth looking at. Others are less lovely. It is worth knowing which anchorages have distilleries within walking diatance — many if not most do tours and I think even those that don't still sell their stuff. So going kind of from the south to the north, and only including anchorages with distilleries near by (which is just about the lot):
Islay: Bruichladdich
Lagavulin (and walkable to Laphroig distillery)
If I were forced to choose between anchorages, I would pick Lagavulin on Islay (for the anchorage), Isle of Jura at Craighouse (for the hotel and general atmosphere) and Tobermory (for the charms of Tobermory). So go for it, buy a bottle of single malt at each anchorage, drink it up over the next year (or day), and then go round again the following year (or day).