For more see City Hotel
The City Hotel is the Sparticles base (Later the Ranchers base) until the episode the Fallout.
The City Library is only seen in the episode the Invasion when Reese goes to see an exhibition on the Sparticle Project.
The University is where Anita lives and where her, Doomsday Dora and Henry Barker (Kat's father) worked. It is first seen in The Message and then appears in The Unsuitables. It is mentioned at the end of The Water Rats with Anita asking the Ranchers to come there for the dictaphone for the door to the Sparticle Project.