Ask Lemmygrad

Logistics: train hubs, river shipping, harbours are all centered around cities. Stalingrad was a train nexus and important for river shipping oil up from the Caucasus.

Industry: That stuff is in cities. Useful to yourself, and the deny the other side.

Fortification: Large complexes can be turned into strong defensive positions. Even a wholy bombed out city provides lots of cover. Large sevage systems allow for hidden troop movement.

Population control: Depending of the grade of urbanisation, taking control of cities means having large chunks of the population in your hand, less people to join the other side, more to work with yours.

Loot: Lots of booty in them cities. Many people close together means more loot close together. Important for the likes of Daesh, Israel or the Nazis.

As for Stalingrad: For the soviets it was a important city, but not central to the war effort. The Axis went for it because of the Name, same with Leningrad. The Soviets commited a staunch defense because it was a good psoition to hold the Axis advance.

The axis advance into the caucasus happened before Stalingrad. When that stalled, the Axis went for Stalingrad to hurt soviet logistics, and because evil Stalin city. The Axisa got kicked out from the caucasus and most of Kuban when the dispersed retreating soviet units rallied, reorganized and rejoined the battle. That lead to a massive numerical superiority against the Axis in the region. A numerical inferior force can hold off a superior one, but not in the steppe without any natural defensive positions like rivers. The axis army in Stalingrad got cut off by soviet far eastern forces freed up as a result of the non-aggression pact with Japan. That pact freed up a lot of well equipped, trained and fresh forces for the Red Army.