In Berlin, the CIA folks seemed to stay in the comfortable hotel while they made Tom Hanks's character stay in a gross, cold, run-down hideout.
Donovan can't stay at the Hilton because it would blow his cover, so to speak. The US and the USSR can't be seen to be bargaining with each other. To preserve Donovan as a private citizen negotiator, he has to stay at a different place.
Aside from plot reasons, having Donovan stay somewhere other than the Hilton makes him a more relatable underdog as he bumbles around Berlin with a cold. It also allows the film to show what Berlin was really like outside the bubble of US influence and the CIA's setup. If he stayed with all the other government officials and traveled with them, you wouldn't see him walking through the bombed out streets by himself or getting his coat stolen.