The North Shore of the St. Lawrence river is really scenic, but only to a point.
So, if you are not afraid of hills, I would suggest riding highway 360 from Québec to Sainte-Anne-de-Beaupré to Saint-Ferréol-les-Neiges, then highway 138 to Baie-Saint-Paul, then highway 362 to La Malbaie.
That stretch is really
hilly, with lots of 14-18% grades that are a few km long. The scenery is gorgeous. If you feel like it and don't mind backtracking, go down to Saint-Joseph-de-la-Rive (warning : steep downhill) and to L'Île-aux-Coudres
From La Malbaie, you could take a side trip in the back country to Rivière-Malbaie (Éric has better instructions on that one)... and then you are back on highway 138. However, East of that point, you'll get all the traffic, limited shoulders and only a few nice vistas. I would recommend that you either take the ferry Saint-Siméon - Rivière-du-Loup or Trois-Pistoles - Les Escoumins.
The first one will bring you earlier on the friendlier and nicer (from that point on) South Shore, but if you prefer to do a whale sightseeing tour, you might prefer to use the Trois-Pistoles-Les Escoumins
(back in service this year, but weird schedule linked to tides.
On the North Shore, there are some nice vistas East of Saint-Siméon and Les Escoumins, but you'll have more on the South Shore.
Also note that if you have some kind of climbing phobia, you should ride on the South Shore all the way from Lévis. While that road is less spectacular than the Charlevoix one, it still is a very picturesque one with lots of history.