I'd like to view mountain and valley villiges While visiting Vienna

My destination is Vienna, where I will meet an old friend who is going to be there on business.
While she is busy for a day or so I'd like to see those beautiful mountains with little villages and lakes ,and all that stuff I've seen in photos.

Can some one give me a few tips on places I can take a train or bus from Vienna in the morning  , and be back later that night ?

Also any of the ski hills have summer skiing? I'm thinking Glacier skiing.
I have a hard time figuring out how to get to and from the many places I see on my google map.

My friend has lots of the finer things to take me to see, museums, classic buildings ,and that kind of things, but I'd like to get to the mountains while I have free days.
Maybe if someone can name a place ,and best way to get to it from Vienna, i'd save time being lost .
Thanks

I just typed in to google  "most beautiful mountain villages in Austria" then clicked on images.
I can't believe what I see.  You have so many !
I'd like to visit them all , but this trip I'm just staying a few days to see how things are .
I'm sure I'll return for a longer visit  very soon .

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