Every capital city I have ever been, and many smaller cities and towns, have shops selling coins, and those mostly also do bank notes of the country.
In German, for Vienna and Germany, you google on 'Münze' or of course 'shops Coins or Numismatics' (leave off the last few letters and google will fill it out for you.
I can not find the Slovak word as fast, is seems to be 'mince' (which might give confusing results on English language search sites) or 'minca' or 'minci' which are less likely to be used in the name of shops, so if you search on "koruna" and "halier" (the name of the coins they used to use) you will likely also find the right shops.
I find two shops for Vienna, that does not mean there are not more, it is just a first, general, search.
Auerspergstraße 5, 1080 Wien
Am Heumarkt 1, 1030 Wien
For Bratislava I found this one:
Coin and Stamp Collecting Shop
Majkova 2 (Avion building, walking distance from downtown Bratislava)
Again, likely one of more, maybe even many.
As the Euro in Slovakia is relatively new and in Austria not that much older if you see it in the light of the whole history, you might even find the old money in souvenir shops, in ready filled packs with a nice collection. I do not remember having seen those packets in those countries, I do remember them from my home country.
How much you need to pay depends on whether the money can still be exchanged for euros, and of course, the rarety and the condition of said money.
I have used this site for Slovakia, and Google search for Vienna.