Best city to base ourselves to explore Europe

I am not sure if it will be happening soon (or ever), but it seems like there could be restrictions coming on apartment rentals in Spain. Just something I'd keep an eye on. That is what the anti-tourism protests are about there--housing prices.
Paris is somewhat reasonable from BCN but those are not short journeys by train. I guess I would put the emphasis on where you want to be overall, then cross-reference with the travel times for the places you are interested in visiting.

Personally I think you need to be more in central Europe -- say Paris or one of the smaller but major cities of France. Get a good map of Europe and put some pins in it to help you judge distances. Both Madrid and Barcelona are far to the south and west. It would not be my choice.

For example a train between Madrid and Berlin is 18 hours and 3 changes. And just as long for other locations. Similar to being in New Orleans and visiting New York city for the weekend. Spain makes no sense.

Spain is lovely and warm but... 2-4 day trips will not get you very far by train, which is why budget airlines have prospered in the last several decades across Europe (and of course in the US too). It is 10 hours by train from Madrid to Paris for example. Check out the website of theManinSeat 61 or Bahn.com for train information. Milan or some other Northern-Middle Italian city would provide a home base that is reasonably temperate and much closer to most of the continent. Have fun planning.

Your itinerary plan is not ideal from Spain. France would work better. But seeing all of Europe from one base is not feasible.
Or focus on Spain and Portugal from Madrid or Barcelona. Or stay in France, exploring some of it’s regions.

Also, 2-4 days is "not enough" for Paris or Berlin, IMO. A better plan is to, as previously suggested, make a list/map of the places you want to visit and then plan to travel from one to the next, making sure to include some places that are intended to be "just" for rest (whether that means a beach or a country or mountain house where you can do laundry and catch your breath). For example, if you fly into Lisbon or Madrid in early spring and start making your way north and east, using trains/planes/automobiles, you could finish in Berlin and fly home from there, having spent time in several places along the way, including Paris and Zurich. I would go in the opposite direction if your trip is in the fall.

These are all great responses. I am now leaning hard towards just moving from “Key” cities we want to visit, spending enough time in each to see most of the sites.
I do appreciate all the responses.

Doesn't make any sense to me. Why would you want to repeatedly take 10-20 train trips back to Spain, retracing your footsteps over and over. Doesn't seem relaxing to me.

If you have four weeks, just stay a week in four different cities.

A base would work if more centrally located. But the key to a base, is that you are spending most of your time there, or doing day trips, if you spend most of your time elsewhere, then a base loses it's appeal.

As an example, on two trips we based ourselves in central Western Germany. The main attraction was that my brother had a house there while stationed with the military (three times in his career) and found it great, with relatively easy access to Amsterdam, Brussels and Belgium, Paris, Munich, Northern Italy, Prague, and Berlin, plus points in between.

I actually considered somewhat duplicating the situation, but basing in Dusseldorf or nearby. That area offers easy train connections to anything within 4-6 hours,(most of Germany, Netherlands, Belgium, Luxembourg, Paris) and a great airport with lots of budget carriers, taking you nearly anywhere in Europe in about the same time or less.

You can also do more of a hybrid thing, pick two or three bases, each covering a wider area.

Opps, I missed one of the restrictions -- late fall, early spring. That is a curve -- further north you will give very short or shorter daylight hours and cooler weather. While fall is cooler, the pm son is low and weak in Paris, Berlin, at that time year and does have some impact on outdoor activities. Early spring is not much better and it6 can be very rainy or at least very cool and damp. Is there is reason for this time period.
Every a month early in October would be a more preferable time. And you need to recognize that going to Europe is not like going to Florida or Southern CA. It is much bigger. Hit your local library and check out some of Steves' travel DVDs and guidebooks to give you a better idea of the framework to hang our suggestions. While it is appealing to have a base, it is realistic to limit your train travel to a max of about two or at the most three hours of one way travel. Lots to see and do. But plan to return in a couple of years to make your decisions easier. One of our best phrase that we have used for 50 years is --- "We will see that next time." And we do.

PS Did you do your Italian trip this year?

For what you aim, BRUSSELS is ideal... international hub to the Americas and not far from Paris, Amsterdam, even Berlin and Copenhage by fast train... and a short flight to London, Oslo, Milan or Barcelona among others. However, temperature-wise (and light conditions) Central Europe can be dull, grey and damp at certain periods of the year.

However, temperature-wise (and light conditions) Central Europe can be
dull, grey and damp at certain periods of the year.

However not in the Spring or Fall. There is no better time to be in Central Europe than October. Clear, cool, dry.

Why try to base yourself in ONE place?

If you do that, you will spend way more time and money on travel than is necessary.
If you like basing yourself, the find more than one base.

If you base yourself in a large city like Paris, Berlin or Munich, you will pay more for lodgings, since lodging cost more in large cities.

For Spain, Madrid works well to visit Toledo, Segovia and Avila on day trips. Still, you would likely want to see Barcelona, Seville and Granada at a minimum.
Travel from Madrid to Cordoba in route to Seville, then from then visit Granada and perhaps Malaga and Rhonda. Fly into one city and out another.

You have a month, so, London train to Paris, train or plane to Prague, train to Vienna, train to Budapest. Thats 5 cities at 5 to 7 nights each.

More exciting and mysterious: Podgorica and a week in Montenegro, transfer (ask, I can help) to Sarajevo and a week in Bosnia & Herzegovina, transfer (again i can help) to Dubrovnik and Croatia for a week, RyanAir to Budapest for a week. Despite all the transfer help needed, not much more expensive than the first suggestion.

Habpsburg Empire tour: equal time in Vienna, Budapest and Lviv ( i can help with the Lviv connection). Maybe end in Prague.

Yes, I am better advice for the quirky tours that become books.

I agree with Enric above. Brussels=excellent advice.
I am done. the end