We have 3 weeks of touring in Denmark coming up the end of August '17. Is it practical to think that we could avoid using a rental car and visit Jelling; Silkenerborg; Ribe; Kronborg; Frederks; by train?
With a combination of trains and busses you can visit practically any place in Denmark, use www.rejseplanen.dk to plan all public transport. However you need to use the correct spelling (Silkeborg). There is no place called Frederiks, but lots of places called something with "Frederik", since it's the name of 10 Danish kings (Frederiksborg, Frederikshavn, Frederiksværk, Frederiksberg etc).
For the sites in Jutland, a car might be more practical, since it allows you to visit some smaller places.
The station (and the city) is called Helsingør (type in "Helsingoer" if you don't have a Danish keyboard)
Your responses were very helpful. My apologies for the misspellings. I am now able to more comfortably use the transportation website. I hesitate to rent a car since I am not familiar with the signage and parking rules etc. Any suggestions on the best way to become better acquainted with traffic rules etc.?