At the time of the First Doctor's visit to the planet, the city dated back from before the Thousand Year War. The Daleks lived not in the city itself, but rather below it where they thought they were shielded from radiation.
The entire city ran on static electricity transmitted through metal floors, which the Daleks of this era of Skaro history required to power their casings. As a consequence of this dependence, the Daleks were unable to leave their city. They were unaware that a group of Thals had also survived the neutronic war.
During the war between the Humanised Daleks and the Daleks ruled by the Emperor Dalek, the Daleks had a city which the Second Doctor, having visited before, knew how to navigate. Fighting between the two groups of Daleks devastated the city. (TV: The Evil of the Daleks)
It is not known definitively how these stories relate to each other chronologically. Inarguably, the Daleks living in the city during the Doctor's first visit had cruder technology. By the time of his second visit, the Daleks could move outside the city and had developed time travel.
Behind the scenes
The Dalek Handbook states that the city was named Kaalann. However, after the Fourth Doctor's intervention with the Creation of the Daleks, the new timeline which was created makes it uncertain whether the city was named Kaalann or if it is the same Dalek city the Eleventh Doctor later travelled to when the Daleks wiped out humanity with the Eye of Time. The Doctor's dialogue then - "Last time I saw it, it was in ruins and the Daleks had fled" - suggests both cities are still the same.
The Target novelisation of Remembrance of the Daleks (1990) states that the Dalek city is called Mensvat Esc-Dalek and is located in the Vekis Nar-Kangji (Plain of Swords).