I've just started working on this, (April 27, 2004)so I'll be fleshing it out of the next few weeks.
If you have from 15 to 20 days to spend on this wonderful island, then, that's ALMOST enough time. What I'd do is this:
I'd take the boat from North Sydney to Argentia. This is a longer trip. I'm not sure of the exact amount of time you'll spend on the boat (I'll check it out and get back to you). In any case, you'll lose two days on that trip, but by all reports it's worth taking once.
Find yourself a nice bed and breakfast in St. John's. Plan a whale and iceberg boat tour, drive around the Marine Drive, visit Cabot Tower and the GeoCentre. That's two days. If you're so inclined, spend a night or two on George Street. There's some great traditional entertainment in St. John's. Ask around to see what's on, and what's good.
Do the circle down the Southern Shore to Ferryland, Trepassey, and back up through St. Mary's. You can do this in a day, or you can find a spot to stay in St. Mary's. You'll see plenty of caribou on this trip, but you won't be able to visit the bird sanctuary unless you go around the cape to Placentia Bay. You can do that on this trip or plan a separate trip.
If you have an extra day or two you may also want to do Trinity Bay. You must take in the Trinity Pageant if you like theatre with a difference. Trinity is a picturesque historic community, well worth the visit on its own merits.
When you're driving across the island there's two side trips I'd recommend. If you go to the Bonavista Peninsula through Cambo, that will take you back on the TCH about 60 or 70 miles further along but it's actually a longer tip than that. I'd recommend you go off that road to Twillingate and you may also want to visit Change Islands and Fogo Island. You'll see many more beautiful small communities. The road is a little rough in places.
After you've passed Grand Falls (you may want to stay there overnight), you should also take a side trip to King's Point and Little Bay Islands. There are several good hiking trails and some beautiful photo ops.
Then go to Gros Morne. Of all the musts in your visit, this is the most must. See my five day trip to get a detailed suggestions as to what you should do on the Northern Peninsula.