All main European cities have cathedrals and most of those use the main organs in the main services. Maybe not every Sunday but almost all of them will have them in use for the Easter and Christmas services.
You will need to research which of the main churches in really big cities will do the best or longest organ playing around the services.
When you look up organ concerts in the city you happen to be in, do not discount concert halls, as some of them have organs that are as good as most of the church or even the cathedral organs. And it they are happy to organize an organ concert, it will be worth your time and money.
I am not a lover of organs, will escape out of a church as soon as the organ starts. The last event was an organ playing while I was still in the RC (Roman Catholic) cathedral in Haarlem, the Netherlands (called St Bavo, as is the old/former cathedral in the same city) and this had been posted locally in the concerts list of the ‘things to do’ website.
In London I would check the concert list as well as the ‘activities’ list of St Pauls, Westminster Abby as well as Westminster Cathedral (which is the RC cathedral for the area.)
In Paris, again the same listings and for all the main churches. I remember my father telling very enthousiasticly about the organ in the Saint Eustache, but he did mention organs in many of the main churches and cathedrals he visited in France. And not just at the main church holidays but also on random Sundays.
In Germany I have only visited one main church, the Dom in Cologne and indeed, it had a main organ and they played it.
In short, each main church in Europe is likely to be worth visiting.