First, wind blows from the regions of high pressure into regions of low pressure.
Why do we see water vapor on the external regions of the cyclone? Because the speed of rotation in these regions is so small that water molecules can attach to small pieces of dust (nuclei, more that 1 micrometer in radius) and form droplets - many molecules of water attached to the nuclei. A large number of droplets (the size of a droplet is 0.02 mm) forms what we call clouds.
The clouds on the external regions of the cyclone never reach the center because the Coriolis force deflects the air masses moving to the center.
Thanks to the Coriolis force, the center "slips" away from the external clouds and results in calm weather and clear sky.