Yes, I was thinking Strasbourg (and I agree about Amsterdam). Perhaps with a stop in Nancy on the way. But none of these suggestions provide any country. Perhaps staying in Paris and taking day trips into the surrounding countryside. This book has some good ideas for day trips from Paris: https://www.amazon.com/Paris-Past-Tr.../dp/0393343154

Five travel days in a 14 day period? In my opinion, that is insanity. Packing, checking out of your hotel, getting to the train station, getting to your next hotel, checking in. Tedious chores ... and you want to do this five times?

You say this is your first trip to Europe. Not your last, I would imagine. Take your time; enjoy and revel in two or three places. Figure on a week in Paris. You will not be able to see and experience a fraction of all there is in the city in a week, but you will get a wonderful taste of Paris. Maybe a day trip to Reims?

Then choose your your other destination. The Netherlands/Belgium? Take the train to Amsterdam. See the museums, stroll along the city streets, take a day trip out into the countryside. Go to Bruges for a day (a day is more than enough to experience Bruges.)

Back to Paris to relax before heading home, knowing you have seen and experienced so much more than a blur of train rides and in-and-out hotel rooms.

And then, once home, start dreaming about your next visit to Europe!

Or visit Paris and then take a train south to Provence for your countryside time, or Alscae, or Norma sy and Brittany. On our first trip to Paris we stayed a week and then spent three more weeks in other more rural areas of France.

What are the dates of your trip?
Where are you flying from?

Yes Strasbourg is neat and Nancy really nice but it's nice to experience different countries too - even places like Amsterdam where in tourist areas foreigners seem to outnumber Dutch but still it's way different than France. and thus Cologne may be nice too yes just because it is in Germany and really close to Amsterdam by train (but a so-so city for most tourists except the great cathedral - architecture like OP says just average and very little old left.