Live in London because it's an English-speaking city that I think I would feel very comfortable in.
Visit Rome because I've never been a fan of Paris (no offense to any Frenchmen here, feel free to change my mind, I'll admit I don't know much of the city). It always struck me as very overrated. I'm indifferent to Madrid and Berlin currently (once again being open to having my mind changed). Rome, though, I've always wanted to visit because of the food and numerous historical attractions (Yeah IK I should be a fan of Paris for these reasons but I like Italian food a lot more and the Colosseum and Vatican always struck me as more interesting than the Eiffel Tower and the Notre Dame Cathedral).
I would rather visit Moscow or Istanbul if they were options, though.
In regards to Paris, what I tell everyone is you basically have two Parises: Rive Gauche Paris (South of the River Seine, where you have the Latin Quarter, Boulevard Saint-Germain, Invalides, etc) and the Paris North of the Seine.
The part of Paris South of the Seine is absolutely magnificent, and makes a visit to Paris worth it. But I agree with you that I don't care for most of Paris North of the Seine either.
I also agree with you that I couldn't care less about the Eiffel Tower. However, I love Notre Dame, it's one of my favorite monuments in the world. I'd take it over the Colosseum or the Vatican any day.
I'll also point out that Paris isn't my favorite French city. My favorite is Lyon.
That being said, I think it's still the best of the major European capitals, even if it has flaws. It has more charm than London and is definitely more affordable.
And I actually found Rome kind of underwhelming. Other than the Roman ruins and the Vatican, I don't find there's a whole lot there. In Italy I definitely much preferred Florence.
Very interesting information!
Can you tell me about any landmarks in Paris that you find underrated that I perhaps wouldn't have heard of?
Also, about the Cathedral (it looks like non-Christians are allowed to visit), maybe you're right as in it'd be a good travel destination.
Some underrated landmarks in Paris:
-The Sainte-Chapelle: in the Palace of Justice near Notre Dame, it's an absolutely beautiful Gothic chapel that was built as the Palace Chapel for King Louis IX. On the inside it has beautifully painted columns and ceilings and also impressive stained glass windows. It's even quite impressive from the outside, but even more so on the inside.
-Place du Panthéon: my favorite square in all of Paris. On this square you have the Panthéon (originally constructed as a church to replace the decaying Sainte Genevieve Abbey, was turned into a secular monument where major figures of the Republic such as Victor Hugo are buried), Saint-Etienne-du-Mont Church (a 16th Century Renaissance church, one of the best in Paris), Lycée Henri IV (most famous highschool of all of France, which contains the belltower of the aforementioned Sainte Genevieve Abbey) and some Sorbonne buildings
-Boulevard Saint-Germain: my favorite street in all of Paris. Has many nice stores, cafés and restaurants, along with two great monuments.
The first one is Saint-Germain-des-Près Abbey, the oldest church in Paris. Absolutely beautiful church of mixed Romanesque and Gothic architecture that is wonderfully painted on the inside.
The second one is the Musée de Cluny. The Musée de Cluny was originally the Roman bath house of Paris (Thermes de Cluny), of which some very impressive and well preserved remains still remain on the site almost 2000 years later (you wouldn't guess it was built by the Romans if you weren't told, the remaining parts of the building are that well preserved) and the remaining part of the site is the medieval city mansion of the Abbotts of Cluny (hence the name) which now houses the national Middle Ages museum.
-Two other churches I very much like, although less so than those I've already mentioned, are Saint-Germain-l'Auxerrois, a Gothic church literally across the street from the Louvre, and Saint-Eustache, a Renaissance church near the Chatelet-Les-Halles metro station.
Then you have some worthwhile monuments in the Paris metropolitan area outside of Paris.
To the West you have the Château of Saint-Germain-en-Laye in the town of the same name. Originally built in the Middle Ages (and still has its Gothic chapel and medieval keep still standing (although the latter was redecorated during the Renaissance and thus blends in very well with the rest of the building), it was reconstructed during the Renaissance by François Ier and is one of the best examples of Renaissance architecture in France. It was arguably the Monarchy's base of operations for 2 centuries (from the early 16th Century until 1682, when Louis XIV built Versailles; the French King usually spent anywhere between 4 and 10 months every year in the Chateau), and two Kings of France were born there (Henri II in 1519 and Louis XIV in 1638; ironically, the latter decided to pick up sticks and move to Versailles). The Treaty of Saint-Germain-en-Laye (the Treaty between the Entente and Austria ending WWI with Austria) was signed here, and it was also where James II of England spent the last decade of his life (he died in the Chateau in 1701 and is buried in the church across the street). It now houses the National Archeology Museum (and has since 1862).
To the North of Paris you have Saint-Denis Abbey in Saint-Denis. The first church in the world to be built in the Gothic style, it's where most of France's Kings are/were buried.
And to the West of Paris, you have the Chateau de Vincennes in Vincennes, a Medieval castle almost next to Paris (Paris' Metro Line 1 ends at the Chateau) with quite the impressive keep.
And to answer your question about Notre Dame, ofc non-Christians are allowed to visit Notre Dame (well, when it's not closed due to having to restore the building ofc).