The primary immunological target of COVID-19 vaccines is the SARS-CoV-2 spike (S) protein. S is exposed on the viral surface and mediates viral entry into the host cell. To identify possible antibody binding sites, we performed multi-microsecond molecular dynamics simulations of a 4.1 million atom system containing a patch of viral membrane with four full-length, fully glycosylated and palmitoylated S proteins. By mapping steric accessibility, structural rigidity, sequence conservation, and generic antibody binding signatures, we recover known epitopes on S and reveal promising epitope candidates for structure-based vaccine design. We find that the extensive and inherently flexible glycan coat shields a surface area larger than expected from static structures, highlighting the importance of structural dynamics. The protective glycan shield and the high flexibility of its hinges give the stalk overall low epitope scores. Our computational epitope-mapping procedure is general and should thus prove useful for other viral envelope proteins whose structures have been characterized.