  In the effective Ising spin-1/2 antiferromagnetic chain system
BaCo$_2$V$_2$O$_8, the magnetic-field influence is highly anisotropic. For
magnetic fields along the easy axis $c$, the N\'{e}el order is strongly
suppressed already for low fields and an incommensurate order is entered above
4 T. We present a detailed study of the magnetic phase diagrams for different
magnetic field directions, which are derived from magnetization data,
high-resolution thermal expansion and magnetostriction measurements as well as
from the thermal conductivity. Zero-field thermal expansion data reveal that
the magnetic transition is accompanied by an orthorhombic distortion within the
$ab$ plane. Under ambient conditions the crystals are heavily twinned, but the
domain orientation can be influenced either by applying uniaxial pressure or a
magnetic field along the [100] direction. In addition, our data reveal a
pronounced in-plane magnetic anisotropy for fields applied within the $ab$
plane. For $H || [110]$, the magnetic field influence on T$_N$ is weak, whereas
for magnetic fields applied along [100], T$_N$ vanishes at about 10 T and the
zero-field N\'{e}el order is completely suppressed as is confirmed by neutron
diffraction data. The second-order phase transition strongly suggests a quantum
critical point being present at $H\simeq 10$ T parallel [100], where the
N\'{e}el order probably changes to a spin-liquid state.
