Harbour Grace, founded in 1517 by Francis I of France, very nearly was the capital of Newfoundland but lost out due to being farther from Europe and more difficult to defend. For long stretches of our history, however, it was nearly as important.
Placentia was the French capital.
Placentia, Newfoundland by
Niels Sampath, on Flickr
These days it's tough to make an argument for it to be anywhere but St. John's. However, if it did move, I think the only possible place would be Corner Brook.
People would start out wanting it somewhere central, such as Grand Falls-Windsor, then the conversation would turn to "Well that's the centre of the ISLAND, what about Labrador?". No one in their right mind would put the capital up there, even more isolated, so Corner Brook on the west coast would come up as the least offensive compromise. Only it's 25,000 residents would be happy with the decision, along with everyone involved with the airport in Deer Lake.