Again, Islay is a good place to find some mildly peated malts, but this is usually in relation to their heavily peated malts, so may not actually be that mild!
Johnnie Walker Black is a good blend to start with. It is rich and deep, with lots of different flavors including a wonderfully wood smoke that is not overpowering in any way.
Another blend with a light smokiness is Monkey Shoulder. This is a fantastic blend that only has the slightest hints of smoke.
In terms of Single Malts, then the Bunnahabhain 12 Year Old is a coastal dram with a delicate hint of smoke and plenty of sweet sherry to compliment this.