I had the privilege of living in St. John's for four years in the late 1950s, when my father was stationed at the former Pepperrell AFB, on the east edge of the city. Remnants of the base can be seen at the north edge of Quidi Vidi Lake (the area containing the two adjacent ball fields), in the map link provided in ATL10A's earlier post.

I returned two times to St. John's in 1984 and 1994, renting a car both times, and enjoyed exploring the Avalon Peninsula. Do visit both Cabot Tower and Cape Spear, as you'll most probably eventually see them both shown later on TV, and you can say, "I've been there!". On my second return trip I drove around the south end of Conception Bay, and stayed overnight in a B&B in the small town of Brigus. I'd suggest you plan to make a similar overnight visit to a small fishing village somewhere on the peninsula, as such villages and their occupants tend to be quite interesting.

Have a great visit, and don't rule out a return.