So many cathedrals! Which one would you pick?

Strasbourg may be the most impressive cathedral I've ever seen. It may be the coloring which sets it apart, but it is the only cathedral I've been to so far that I've wanted to visit twice. Cologne is huge and impressive, but I didn't find the interior ask that interesting. A tour may have helped.

I am sure Notre Dame in Paris is well worth a visit. I have seen the one Cologne, Strasbourg and Paris (before the fire).
Cologne is not my favorite. It has the twin spires that were completed in more modern times, not medieval. I would rate it the lowest.
Strasbourg was special.

If you visit the UK, I there are several worth visiting:
St. Paul's in London, also. Westminister Abbey
Winchester Cathedral, Salisbury Cathedral, York Minster Cathedral, Durham Cathedral, Canterbury Cathedral.

Strasbourg, for sure.

Another vote for Strasbourg. It is gorgeous both inside & outside. We didn’t do a tour - just enjoyed the beauty of it.

If you’re visiting those cities anyway, it would be a shame to not visit each of their famous cathedrals— except perhaps Paris, not because the newly restored Notre Dame isn’t worthwhile, it certainly is, but because there is so much else to see in Paris competing for your limited time. So if I had to skip one it would be that one. A cathedral visit doesn’t need to take much time —- you certainly don’t need to take a tour — and each of them is centrally located in their cities. Actually the best one in Europe, in my opinion, is Chartres near Paris, because of its magnificent stained glass, but that would need at least a half day trip out of the city to see.

I agree that you don't need to take tours, and since they are all central, popping in for a few minutes should not be a problem. It would be a shame to miss any of them, and they are right there. I would, however, add a different church to your list--St. Ursula in Cologne (about a 10 minute walk from the main cathedral) for its bone chapel. Fascinating.

Slate and HowlinMad are correct, that you really don't need to take a tour for the cathedrals. You can spend an hour or less at each one, unless you are a detail-oriented architecture fan. Except for a few cathedrals (St. Peter's e.g.) a one-hour walk around is enough for me. Of course, to each his own. I wouldn't skip Notre Dame in Paris. And if you must choose from the others, Strasbourg. One point, however, is that the cathedral in Reims is the site of the crowning of nearly every French king going back many centuries. I believe you can check them all out without cathedral overload. (And I know how that can happen!)

From a view of historic relevance I recommend to consider also the imperial cathedrals in Worms, Speyer and Mainz. Very much unknown to tourists is the 6-tower basilica of monastery Maria Laach which is known as one of the most beautiful and best-preserved Romanesque monuments in Germany.

Thanks, everyone, for your input! I expect we'll pop in at all the cathedrals but focus on Strasbourg for an actual tour. There appears to be a good audio tour.

If you do visit the Strasbourg cathedral, you may want to consider scheduling your visit to see the astronomical clock in action. Once daily operation, I found it fascinating.

Many cathedrals--probably virtually all cathedrals with an entry fee--have either a simple, take-away folder describing key elements of the building or a laminated handout you can borrow and carry around during your visit. The most important churches are likely to rent an audio guide also or instead.

I'll be traveling in June too. Outside of Paris and seeing Notre Dame I would recommend Strasbourg.

If you want to include Germany, I would suggest Ulm, Magdeburg, and Naumburg an der Saale for cultural, historical (! !) and architectural reasons.