Which would be the best country to visit in Europe during November?

Spain is in the south.

London. I don't know about hostels there, although I'm sure there are some. No one goes to London for the weather regardless if it is June or November. There's endless culture, and almost every major museum is free ( although a donation is always appreciated)

We have been to Europe the last 2 Novembers and enjoyed everywhere. Rome and Italy were very pleasant weather wise 60s F everyday and few crowds. But we were also in Paris, Amsterdam, Germany, Belgium and Prague. Everyone's definition of too cold is different, but most days in Prague and Germany were in the 40's, Paris and Amsterdam in the 50s. You will lose some of the summer experience of lingering at night on an outdoor patio. But, later in November you may gain the experience of Christmas markets and drinking a hot drink among festive locals or the buildings lighting up on the Grand Place in Brussels. There are also more cultural experiences such as classical music almost every night in Prague. it get dark early, but the cities are lit and festive so its no too much of an issue. And crowds are way less in many instances for major sights and easier to meet locals with fewer tourists around. So pick a city based on what you want to see. If cold is a huge issue stay a bit further south like Italy or Spain, but Paris and London aren't that cold.

Well anywhere with beaches, you're not going to get the same winter / summer experience.

But I think Spain would be great, or southern Italy. Barcelona had very comfortable temps when we visited last December.

We used to visit London, and even Scotland (Edinburgh, Inverness, Aviemore) in late Nov./early Dec. for many years. I loved that there were very few crowds! There is still lots to do... museums, markets (regular and Christmas markets), Kew Gardens (yes- even in Dec. they are lovely and their shop is wonderful for Christmas gifts), theatre, concerts, and much more. Day trips are easy on your own by train or coach (bus). Bath and York and Cardiff Wales have great Christmas Markets and are easy to reach by train.

We also loved Austria at that time. It is colder (we even had lovely light snow one year), highs might even be below freezing- but you just dress for the weather, and enjoy the grog or hot chocolate (mit schlag- whipped cream) at the Christmas Markets-- LOL! Again- plenty to see inside if weather is bad. Salzburg and Innsbruck were our favorites, but Vienna is good, too.

Thanks everyone for the responses, definitely helps and gives me a good idea! I will look further and finalize!

Anymore suggestions from anyone, please let them come!

Spain, Italy and Turkey are set up for year-round tourism. Greece kind of shuts down in late October, I'm told. Farther north than that, you are likely to hit winter weather. But the big cities are classic in any weather. London/Paris for a week is much the same experience in November or June.