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Frankfurt and Cologne are super boring cities, with nothing to see outside of Cologne Cathedral.
German big cities generally aren't that interesting. Berlin is interesting but ugly; Munich is semi-interesting but not too ugly. Almost all the other really big German cities don't have much for tourists.
Germany's beauty is in its small towns, villages, and rural landscapes. It has some of the most charming villages on earth. It also has great university towns, like Marburg, Tübingen or Heidelberg. But you will be very disappointed if you spend most of your time somewhere like Frankfurt, which might as well be a European Dallas.
If you're a group of 3-5 people I'd recommend renting a car and driving. It would likely work out to be the most-economical option (definitely cheaper than train or plane), and you can travel on your own schedule and easily explore smaller cities and less-touristy areas. Highways in Germany and NL are some of the best in the world and drivers are careful.
If you're dead-set against driving, consider buses. Much cheaper than trains or flying.
We never experienced any safety issues in Germany or NL, but that was before the recent influx.