So where does Uldah's wealth come from?

They are built in the middle of a desert. The only thing that speaks to me of "wealth" might be the mine they have in western thanalan. That's it as far as I know.

What did all these rich ulduans get wealthy from? It certainly wasn't conquest.

Merchants.
Also pretty much all of N Thanalan, I think Amajina etc is located out of Ul'dah? Right?

Bu merchants...travelling merchants.

Mining plays a huge part in it as well - specifically mining precious metals like gold, mythril and iron (why else do you think the MNR's Guild is based there?). But yeah, it's the centre of trade in Eorzea and thus little wonder it's government is really a corrupt plutocracy (aka, the Syndicate).

Aska and Enki are both right.

To see where a city's wealth comes from, you might be overthinking it if you go beyond a cursory look at their guilds (what the guilds say they do, not what you actually craft with their recipe books - you craft for adventurers, not a city's prosperity).

Limsa Lominsa builds ships and rules the seas. Their ability to navigate and retrieve resources from all over the realm has led them to create some of the strongest equipment and most delicious foods (never underestimate the value of spices pre-globalization). Gridania's ability to live in harmony with the Elementals in the Twelveswood, and their respect for the resources that come from that forest, have made them masters of leather and timber, used in everything from airships to housing to weapons and transportation. Their knowledge of plants for both medicine (Ul'dah) and cooking (Lominsa) is also highly lucrative.

Ul'dah, yes, is in a desert. But that desert is rich in metals, gems, and (for people for whom aetherytes are not an option) the city is also positioned right in the middle of a lot of the most convenient travel routes, which makes it a trading hub. Utilizing that hub to control the flow of trade, the merchants there have managed to manipulate the flow of goods in and out of the city in such a way that Ul'dah pretty much sets the standard of value (and fashion) for the realm. Lolorito's vast wealth stems from the East Aldenard Trading Company, for instance. They even traded with the Garleans up until more recently; it's all interconnected for them.

Even in Ul'dah - the center of fashion - where the jewelry is Eshtaime's (mined by Amajina's), and the garments are Sunsilk's best cloths woven from plants spanning the entire continent - you can still assume for damn sure that the shoes are made with Fen-Yll's leather and Lominsan ships were involved in the movement of goods. There's a reason Lolorito rebuilt Vesper Bay.

Also Ul'dah has access to ceruleum, which is what the garleans used to purchase and the substance as revealed in the Hildebrand quest line is worth a lot.

The same way other real world cities in the desert became wealthy. Trade

Trade. Also the fact its location sits right in the middle of Limsa and Gridnaia.

It's centralised location also means it's got probably got a pretty lucrative high-end tourism industry, between the Colosseum and the Gold Saucer and I guess maybe the Platinum Sands if that's still even open.

I'd like to point out something from the biology perspective that hasn't been noted yet, forgive me for getting into real life examples, but a desert is defined by annual precipitation.

California's Central Valley, one of the most productive places for growing food on the planet, is classified as a desert for 1/3 of the year because it gets lower precipitation than true, year-round deserts during the summer time due to its climate.

Because something is a desert does not necessarily imply lack of productivity. In fact, most deserts have extremely large amount of energy transfer at night; most true deserts are not balls of sand like you see in movies. Especially considering that much of Thanalan does seem to be nutrient rich. It's only really South Than that is difficult to use. Sand is terrible for most plants to grow in.

Living on areas with low to very low levels of precipitation is quite common in human history as well, even in the modern day.

The point of this all being that you shouldn't dismiss a desert as not being profitable simply because, to you, it looks like a ball of dirt. As many large corporations are learning now: that is a very costly mistake to make.