Flying to the chalet:
Krakow (Poland) - 1 hours 50 minutes away.
Bratislava - 3 hour 30 minutes
Katowice (Poland) - 2 hours 50 minutes.
Budapest(Hungary) 4 hours
Vienna(Austria)- 4 hours drive

It is possible to take a train from Bratislava to Liptovský Mikulaš(direct train from Prague, Bratislava, Budapest,Vienna) and then a taxi to the chalet although car is advised.

A further option(for those who want to see one of cities nearby) is:
-fly to Vienna with BA or Austrian and then 4 hours car or train journey
-fly to Budapest with BA or Malev and then 4 hours car or train journey
If you would like to combine mountains with short city seeing this can be excellent option.

Please be aware that snowchains are necessary in winter months!