It's a mixed bag. Our main highways are generally in the interior - either of the bulk of the island, or its various peninsulas. But the little coastal routes that branch off all of these are great.
If there is a road on this island I haven't driven, it's not on any map. Of all of them, the one I would most recommend to tourists is of course the Viking Trail through Gros Morne National Park. It's Norway-quality scenic. And even the side routes, like the one from Rocky Harbour to Trout River, are breathtaking.
But say if you had two weeks here and had already done that on a previous trip, my personal favourite is the drive from Jacques Fontaine to Harbour Mille. There's just something especially lovely and beautiful about it. The roads are wide enough for two cars to pass comfortably, but they're still tucked into the folds of the landscape.
(This also explains what I mean about the highways. That main route in the middle, the Heritage Run, is in the centre of the peninsula. There's nothing there -it's like driving to the moon. But take any turn off, and you'll end up on a local coastal route like the Harbour Mille example).