Since 1328 was Kremnica one of the most important free mining cities. Even the miners were here ages before. In the same year was established also the Kremnica Mint which is since then continuously working. It means almost 700 years.
All the necessary information about exposition of Kremnica Mint are here.
The history of gold mining is shown in Adit Andrej exposition. The visit is about 90 mins. And fee is for adult 4 Euro. you have to go little bit out of the center.
More detail about Adit Andrej exposition are here.
The heart of the city is created by mansion houses around the whole square together with fortification. The most dominant is City castle with the Church of St. Catherine. Also here is museum and you will have the most beautiful overview of the city. On the square is also St. Trinity column (plaque) from 18th century.
In the mansion house 10/19 is Museum of numismatology.
More details about all these attractions you can find here.
Kremnica is one the cities you will feel the history in every step. It is the city with heart and you simply have to love it.