Maybe a bit late given the date of your post and that you're going this month sometime but in CPH recently, I decided to go for an Airbnb (my first time). The hotels there are expensive and nothing appealed. The Airbnb was great - a big spacious flat on a street in the middle of the city.
As for sightseeing in TXL and CPH, it really is down to your preferences with the usual tourist top spots in each city. (Out of the two, I found Berlin much more interesting but YMMV.)
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