Vancouver is nice though rainy. You can go up into the Rockies to see beautiful scenery - Lake Louise and other places like Japser... then down on to the plains to Calgary... take a train across to the east coast maybe: Quebec and Montreal, both French-speaking, Toronto and Niagara... then out to the Atlantic states, Nova Scotia, Prince Edward Island, Labrador... In 3 months you should actually be able to see plenty. You could even get to the Klondike where the great gold rush was (in the far west), or up to Hudson Bay to see polar bears. Very big country and mostly empty.
Good dinosaur museum out in the badlands 80 miles or so from Calgary
http://www.tyrrellmuseum.com/