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14 days trip to europe (London-Amsterdam-Brussel-Luxemburg-Paris.), please help with itinary

I will be traveling to Europe alone in the summer, from July 31-August 14 for 14 days from Houston. I plan to visit North European countries for the first time. I have decided to go to cities are not too far apart meanwhile have plenty to see: London-Amsterdam-Brussel-Luxemburg-Paris.
Experienced European travelers: please help me decide if this itinerary is reasonable/plausible, time wise. I would like to have a taste of major cities. European trip is not cheap, so I would like to maximize my days but meanwhile won't be spending too much time just on traveling either .
Any suggestions would be appreciated. I am a middle aged woman, shows, clubs, concerts etc, are not on top of my list. I am interested in history, nature, arts/museums.