Take the C32 East (and north) to the BV-5126, which should take you into the heart of Calella. You won't have to go into the city streets, if that's what you mean.
El Prat airport is south-west of central Barcelona and Calella is to the north-east, so you'll have to find a way of crossing the city.
If you've not already booked your flights, opt for Girona airport rather than Barcelona. It's closer to Calella, which is easily reached by driving straight along the N11. Ryanair have dirt cheap flights to Girona from Prestwick, Newcastle, Tees Valley, Doncaster, Blackpool, Liverpool, East Midlands, Bristol, Bournemouth, Luton and Stansted.