There are many cities in Europe, which are worth a visit - or even many visits. You've already experienced nice ones like London, Paris and Copenhagen. I think, you won't be disappointed with Amsterdam, Rome or Berlin.
No reason to worry about the location of the WA in Rome. I recommend guided tours by Segway or bike there (i.e.
www.rex-tours.com). Great with teenagers. Berlin is maybe a better choice when your kids are older teenagers. The Hiltons there are ok, but not the best ones. I wouldn't stay at the WA Berlin with teenagers. WA Amsterdam is from my point of view one of the best three Hilton properties in Europe.
In the last 10 -20 years the main tourists spots of big cities look more and more like the same. So I recommend to see the special places there as well. I.e. if you only stay at La Rambla in Barcelona, it's not so different to some place in the US. But you won't find the Sagrada Familia anywhere else.
From my experience AirBnB is the better choice, especially when needing two rooms. You can save a lot of money or you can get a much more impressive apartment. But of cource you can't pay with Hilton points there.