What are four big ways for a region to get rich? Have resources, steal resources, manufacture goods from resources, and be a place where outsiders come to trade resources. We see all of those in the circum-Mediterranean world: Western Europe, North Africa, the Near East, the Byzantine Empire.
Well, the first one doesn't always work out so well in practice (see also: cities versus countryside). The second one...on a large scale, formal imperialism/colonialism is still many centuries away. On the smallest scale, sure, individual lords are stealing resources from each other's lands or ruining each other's resources or just straight-up stealing land (a major measure of wealth), but that's endemic rather than concentrated in any specific region.
Don't get me wrong--having some kind of natural resource, be it wool or saffron or swordfish, is definitely a boost to a region's economy. But if you're a countess with a choice between pastures and pastures of sheep or vibrant spinning and weaving industries, it's not a mystery which one will bring in more tax revenue.
For 1000 CE, I know a lot more about trade than manufacturing, and trading centers were also generally were the money was. So that's what I'm going to concentrate on.
So in this Europe-North Africa-Near East sort of triangle-ish world, the two kind of sweeping, have-many-exceptions statements are: (1) the closer you are to the Mediterranean, the richer, and (2) the Islamic world is way better off than the Christian world, and Byzantium and Christian Italy are way better off than the rest of Christian Europe.
In fact, in 1000, the Latin Christian economy is...well, I like to think of it as "finally getting out of bed in the morning". The early medieval western European economy wasn't dead, it wasn't even necessarily asleep. But it definitely didn't have its act together like it would after the 10th century or so. But except for some of the Italian city-states, it's not quite there yet in our period.
"City-states" is key here: the wealthy areas are cities, as centers of trade and manufacturing. Genoa, Pisa, and Venice are the big-deal Christian Italian city-states in this era. And they are definitely economic rivals, especially for trading privileges with Byzantium and with Sicily (which is under Muslim control at this time).
Sicily, meanwhile, is one of the places to be in our Triangle World, especially the cities of Palermo and Messina. Now, Sicily is also rich in natural resources around 1000 CE--aforementioned swordfish, also tuna (I'm not sure whether those are actually the major raw commodities, or whether those were just the two that amused me so much I wrote them in my notes). And rural Sicilians were pioneering new technologies of hydraulic irrigation that was increasing agricultural productivity, too. But for the most part, Sicily's wealth is growing because it's so accessible for trans-Mediterranean trade routes.
In Iberia, wealth is heavily concentrated in the Islamic majority/southern part of the peninsula. And here, it's also primarily in cities. Most of these are along the coast (Seville, Cartagena, &c), but others are more inland but accessible by river (Cordoba). From the 900s-1100s, southern Iberia--al-Andalus--does very well financially as a conduit between the Islamic and Christian economic worlds, between the Mediterranean Sea trade and the Latin European overland trade.
Notably, you have a lot more Christian merchants going to Islamic cities than vice versa. It's not a lack of contact, either--there are pretty strong diplomatic ties between Andalusi cities and Constantinople. Just, not a lot of direct trade. Venice, which cultivated strong ties with Byzantium, is an important economic mediator there.
And while a lot of the traded goods in al-Andalus are what you'd expect, I want to highlight something especially cool: around 1000 CE, al-Andalus linked up with the trade in gold and salt from West Africa.
I haven't talked as much about North Africa yet, and with some good reason. In terms of climate and sea friendliness, the northern coast of the Mediterranean is much easier than the southern. So ships hugging the coastline (as they did, because of resupplying and because of the dangers of open sea travel) were more likely to go north than south. Nevertheless, North Africa did have plenty of cities with their own ties into the trans-Mediterranean network--especially for Muslims' ships (see also: Muslim traders didn't travel to Christian cities as often).
Towards the eastern end of the Mediterranean, things start to get really exciting, with Egypt and Byzantium in particular rolling in the money. Alexandria in Egypt, as a port city, does especially well as a transition point between the Asia trade and the Mediterranean trade
So there's your "breathless gallop" view of the circum-Mediterranean economy as the end of the early Middle Ages. Probably appropriately breathless, when you think about Pisan merchants trying to play the Holy Roman Empire and Sicily against each other for their own profit, and Cairene street merchants shouting over each other in the marketplace!
Constantinople, capital of the Byzantine Empire, was in the midst of a massive resurgence under the rule of Basil II of the Macedonian Dynasty. They had been reconquering the Balkans, Bulgaria, eastern Turkey, Antioch, and parts of the Middle East for quite a while now, and the gold tribute and taxes had swelled their coffers. Lars Brownworth's book on the Byzantines noted that in the Emperor's palace, guests were treated to fountains of wine, ate on reclined couches Roman style, and were offered food from platforms that descended from the ceiling. The city had about 300,000 people at this time.
Cordoba in Spain was perhaps the largest city in the world in 1000, under the rule of the Muslim Emirate of Cordoba. The Great Mosque of Cordoba was built around this time, and the city had about 400,000 inhabitants and was a center of industry, trade, and knowledge. Cordoba's 80 libraries/universities were the envy of the modern world, ranging on topics from botany to medicine to astronomy. I've seen Cordoba referenced as one of, if not the, largest city in the world in 1000CE.
Kaifeng was the capital of the Northern Song Dynasty in 1000, with a population estimated to be also about 400,000 and also guessed to be the largest in the world at the time. The Song dynasty reunified China, and with that, the flows of trade, culture, industry, and science would have converged on the capital. It was during this time the Song would have been experimenting with gunpowder formulations, but were mostly using it for alchemy and fireworks. Eventually, they did turn it into military applications.
The Holy Roman Empire in Germany was rather large by this point, so you could probably find wealth and opulence in various cities throughout Germany. The Vikings had been sacking cities for about 200 years, though, so it was not as brilliant as it could have been (the Vikings at this time were also in North American in modern Newfoundland).
The Khmer Empire in Cambodia was also in full swing, having established a new capital and built the Ta Keo Temple in 1000. Their empire was experiencing great trade and prosperity, and with that, a strong culture that resulted in many temples. Many people today visit Angkor Wat as tourists along with the many other temples and complexes that still stand today.
The Fatimid Dynasty in Egypt was doing quite well in 1000, presiding over trade between Europe and as far away as Song China. They had just founded their new capital city Cairo in 969, though cities such as Fustat were still immensely large and important for trade and industry.
All in all, these wealthy areas of the world in 1000 all had something in common: stability and legitimacy. The population largely saw the leaders as legitimate, which creates stability. Commerce and trade thrive in stability and predictability, which creates vast economic surpluses. This in turn helps culture flower and can fund things like temples and luxuries, as well as the military. The military can further enrich the situation, or at least enforce its status quo.
What is interesting in looking at the year 1000 is how content these areas were, but also that many of them would collapse soon after. The Seljuk Turks would come ripping through Iran, Iraq, Armenia, Turkey, and the Middle East within 50 years and begin conquering everything, including defeating the Byzantines at Manzikert in 1071. The Khmer and Egypt would soon undergo civil strife and pressure from abroad. Cordoba was under pressure from the Christian Reconquista of Spain.
I wanted to clarify part of my post. When I say wealthy areas, I’m looking for specific geographic areas and not whole empires or countries. So if one of the answers is Holy Roman Empire, I’m looking for information on why X city or region of the HRE is wealthy at that time.
If no trouble, please also consider the Americas as well as Eurasia that I mentioned