We went for only three weeks and saw a great deal. But I'd stay at least a month next time and be open to lingering when we find a great spot. A whole summer would be great.
I planned our trip very carefully and stuck to the plan because we had scheduled about five visits (not overnights) with my husband's relatives all around the island. His late mother was born there on the Baie Verte Peninsula near La Scie.
You probably already know that Newfoundlanders are warm and welcoming. A great many have Irish roots because men came to work in the fisheries in the 1800s. An excellent museum called The Rooms in St. John's tells the history. A lot of the small coastal towns like La Scie were "Outports" that could only be reached by boat and had no electric, phone, etc until the 1950s when some were connected by road (others were closed by the government and the people relocated.)
I wrote an article about our visit that was published in MotorHome Magazine last year. If you'd like a copy, send me a private message with your email, and I'll email it to you.