Another vote for Lagavulin, here. Actually, a vote for any of the half dozen Islay single malts, with a slight reservation on Laphroig, definitely an acquired taste. The medicinal taste in Laphroig from the iodine in the sea spray affects the peat, and it takes a little getting used to.
There is an interesting "blend" of the six Islay single malts available now. It's called Black Bottle, and it's around $40 at Twin Liquors in Austin. It's a nice way to experience the Islay flavors without having to pick one if you're new to Islay.
There is also a fairly new single malt Highland whisky called Ben Riach on the market. They make a fairly peaty whisky that mimics the flavors of the Islay single malts. The Ben Riach distillery has been in business for over 100 years, but for the first 90 or so they sold to the big blends like Johhny Walker and Chivas. A few years ago, the younger generation decided to give the single malt trade a try. Opal Divine's at Penn Field had a tasting a year or so ago and that's where I learned about it. Their line runs maybe $10-$15 less than the big names. Specs, Twin and Beverage World on IH 35 carry it.
I'm also a big fan of Abelour. Very nice for the price.
And, there is always a bottle of Glenfiddich in my house. I know, I know, they have been much maligned for several years now, but this is the "family whisky." It seems, as the story goes, the "16 men of Tain" distilled their first batch of whisky centuries ago when they rented several copper kettles from a Mrs. Cummins. Being a descendent of the "Cummins Clan" I've got to patronize the family brand.
I had been drowning the sorrows of the Elite Eight loss to Memphis with wine, but I think I'll finish it off with a "wee dram" of Lagavulin after all this typing.
Slainte!