I have done 2 Catalonia tours and know the BCN area very well but I afraid I am not much help for a route. I don't know what a Garmin is and for such small area/tour I don't even take a map, I speak ok Spanish and know "roughly" whereabouts I am, I like to wing it.
OP.
You can easily cycle into BCN via Gava from the airport, only encountering difficulty as you hit the City ring roads, where I head for Montjuic/Poble Sec.
You can cycle pretty much traffic free along the sea front from BCN to Mataro (maybe further?) before going inland.
The coast road BCN C31 to Sitges is a fantastic, if gruelling ride.
The coast road south and north of BCN is horrible, apart from the views for the above ride, I'd avoid it.
It is dangerous.
Girona, Vic & Terrassa are well worth seeing, so make a loop.
B roads can be incredibly quiet compared to the UK, you'll have a great time.