Basics of Life
Cities don't just happen. They exist where the basics of life are readily available. Whether or not the basics are there naturally is a matter for the history of your setting, but they must be there. You need...
- Water - I hope I do not have to explain why
- Food - Ditto
- Shelter - You need to be able to build homes; If there are no local building materials, you cannot have a city. You will have an outpost at best.
- Access - You need to be able to easily move in and out of the city. Cities in mountains rarely thrive without advanced transportation technology.
In the case of your desert city, you would need water (a river or springs, though it does not need to be enough to support the current city, just the first settlement), you need enough arable land to support that first settlement's need for food. You need access to wood or grasses to make structures. You need roads and/or rivers to travel on, which as you mentioned, would be the point of the city.
The first settlement needs a purpose. Just being at a cross-roads is not enough - not every junction of the inter-state is a massive city. That location needs to serve a purpose. It must have a natural or artificial resource that a traveler would need. In my opinion, water is the most logical answer, however other needs are possible, including precious metal and mineral mines.
There needs to be enough engineering skill in the city to build infrastructure - irrigation, aqueducts, roads, sanitation, etc. These are more important in a desert than anywhere else. A small spring, which would be enough to support a small settlement would not support a large city as it grew - technology is how a city would solve that problem. Do not forget that cities themselves are systems of technology; the land would not naturally support that many people living in the same place. This would be an important point in your city.
Example: Las Vegas
The city of Las Vegas was formed as a small outpost on the road to the west (during the expansion of the United States to the west). It remained that way - an outpost for water and animal feed (and later gasoline) until the great depression, when water (from the brand new Lake Mead created by the hoover dam) became more abundant, with it came irrigation to grow crops and raise pigs. Shelter came in for form of artificial resources moved into the area by the government for the construction of the dam. With only these three, the city was a boom town in the classic sense - it served as a place for dam construction workers to waste their paychecks on vice. The city itself did not grow until the final basic of life was accomplished - access in the form of the national numbered roads system ('Highway system'). Without these four things, and technology to more efficiently use the four things, you cannot have a city, especially in a desert.