I've cycled acros Canada twice, taking different routes. The first time I took the Trans Canada from Vancouver to Calgary and meandered through some small roads in the Prairies on my way to Winnipeg, then went across the north shore of Lake Superior. Last year I took the Yellowhead through Edmonton and Saskatoon, and then crossed into the USA along the south shore of Superior.
There is a big difference whether you go across the south or the north of the Prairies. The south has more interesting towns but the north has more varied scenery and landscapes. Unfortunately, a lot of the small towns in the Prairies are pretty depressing, they are tearing down wooden grain elevators and consolidating services in larger centres. If you intend to avoid the TransCanada east of Calgary, I enjoyed riding out to Drumheller (awesome collection of dinosaur bones) and then crossing into Saskatchewan at Alsask towards Rosetown. From there you can cycle towards the massive Gardiner Dam (one of the largest embankment dams in the world) which holds back Lake Diefenbaker. Traffic will be super low on the roads that cut diagonally from Elbow to Moose Jaw. Moose Jaw is really interesting, make sure you soak your tired legs in the mineral pool at Temple Gardens and take at least one of the tunnel tours.
Cycling in Manitoba is terrible all around but if you take SK13/MB2 from Weyburn SK to Winnipeg, It would probably be one of the better routes with nice small towns . Many of Manitoba's highways have no shoulders, so get a good mirror and watch out for trucks.
It is really tough riding in Northern Ontario, the climbs around Lake Superior can be steeper than those in the Rockies. It is well worth doing once, though. When you get to Sault Ste. Marie, go to Velorution bike shop to ask for advice heading east. They have a quiet route that meanders through Mennonite country and skips the busy highway at least up to Sudbury. They also have a free campsite in the back of their store. There are a lot of options depending on whether you decide to go to or skip Toronto. I'm in the Ottawa area, let me know if you need specific advice on the area.
Cycling in Quebec is much more convenient with the Route verte system which goes to practically every region of the province. As for New Brunswick, I particularly liked cycling through the Acadian shore (Campbellton-Shediac) better than the St John river valley (via Fredericton). It is more off-track and gets you close to the bridge to PEI.
Cycling the long way through Newfoundland From Port=aux-Basques can be tedious, so if you decide to take the ferry to Placentia instead, ride around the south of the Avalon Penninsula via Cape St. Mary's to get a good taste of island life before heading to St John's.