For good views, Signal Hill in St. John's is the obvious one close to downtown. When you're up at the tower, there is a choice to walk back down the way you came up or go down past the Queen's Battery. Take the Queen's Battery path for a nifty view into the narrows and the harbor on the way back.
If you go out to Cape Spear, you've not only got great views, but you can see back to the tower you were at on Signal Hill.
Not quite the same kind of view, but at Cape St. Mary's Ecological Reserve there is a spectacular sea stack covered with nesting seabirds just off the cliff where you are standing (after walking through the lovely sheep pasture from the visitor's center...). The birds actually glide all around you while you are looking.
We also took a boat tour out of Bay Bulls (we used O'Briens but there were others) that go to the offshore ecological reserve. The boat gets quite close to the puffin nests on one of the islands, and we also had the opportunity for humpback whales that day.
Beautiful, beautiful country...