If you want to try peaty, not too expensive but very good try the Laphroaig 10.
Add just a slight amount of water, and let it sit for a few minutes - this really lets out the sweeter flavors.
Otherwise, it is VERY peaty, you can taste iodine and seaweed, but the sweetness of the malt really balances it out. It's one of my (and my wife's) favorites!
Another good Islay peaty single malt that won't break the bank is the Bowmore 12, it is peaty, but has a crisp, clean tast to it.
Hi from Western CO!
Nothing better than a Single Malt flask while on a chairlift