The stretch between Caleta and Torre, at Caleta end or a little further along the coast to El Morche. The beaches at Algarrobo and Mezquitilla are small and quite nice (Alagarrobo has a newly refurbished paseo), but may not be as sandy as you would like.
It does tend to be the larger beaches that are sandy and obviously they are not the quietest.
Sundays during August tend to be the busiest times. This is when they are frequented by large Spanish families who take everything, including, I'm sure, the kitchen sink. I've even seen wedding receptions held on the beaches here. This is of course all part of the charm of this area.