There are a bazillion places to ski in those countries. I've been to
Davos, St Moritz, Ramsau, Seefeld (near Innsbruk) and a few others.
Any of those should have what you need. Ramsau is in Austria, an hour
or so east of Innsbruk and at the base of the Dachstein. That's my
choice.

As far as skiing in "Czechie", I'd pass. I know that they havr some
places north of Prague, but I'd opt for more developed areas of Europe
if it is your first time.

bt