Strong confinement, in all dimensions, and high mechanical frequencies are highly desirable for quantum optomechanical applications. We show that GaAs/AlAs micropillar cavities fully confine not only photons but also extremely high frequency (19-95 GHz) acoustic phonons. A strong increase of the optomechanical coupling upon reducing the pillar size is observed, together with record room-temperature Q-frequency products of 10^{14}. These mechanical resonators can integrate quantum emitters or polariton condensates, opening exciting perspectives at the interface with nonlinear and quantum optics.