The Solar Apex is the direction the Sun is moving as compared to the Sun's Local Standard of Rest, i.e., as compared to the stars surrounding the Sun. Since all these stars are orbiting the Milky Way, the solar apex does not show the Sun's Milky Way orbital direction, but rather the Sun's divergence from an averaged orbit of the nearby stars.
Recent determinations of the solar apex still diverge by degrees, but a cited value (to indicate the general region) is Right Ascension 18h28m0s and Declination 30deg., with the speed on the order of 13km/sec. This velocity is termed the Solar Motion (Peculiar Velocity of the Sun, i.e., compared to the LSR).
The Solar Antapex is the opposite direction on the Celestial Sphere, i.e., the analogous direction from which the Sun is coming: right ascension 6h28m0s, declination -30deg.