Since you mention a number of the Walker blends, I'd guide you to try a number of the single malts in the Diageo stable and/or are the malt hearts to their blends. Smoky with a little oiliness is Talisker, lighter-sweetish fruity Speysider is Cardhu. Also look for Clynelish (JW18), Oban, Caol Ila, Cragganmore, Glendullan, Knockando, Glenkinchie, Dalwhinnie, Lagavulin and Lochnagar.
I like Royal Lochnagar but they're quite hard to find in the U.S. Clynelish bottles vary greatly, the best bottling I've had is an 11 Year, Gordon & Macphail bottling. Glendullan, bottled under "The Singleton of Glendullan," is a simple malty-fruity Speyside. Cragganmore is richer in body has interesting undertones of candied ginger, to me. Dalwhinnie is lighter and drinks somewhat like a heavier lowland whisky (if this makes any sense) - delicate flavors, as you expect with Glenkinchie.
If you live near a good whisky bar, something from at least 10 of these should be on their list.