I searched for synonyms of workroom but dict.cc just offers working room or study room. I think working room is inadequate for avoiding repetitions, because it is pretty much the same and I suspect that study room is not really the same as a workroom?!
Additionally I was really disappointed by oxforddictionaries.com not finding a single synonym for workroom.
I have several places in my text where workrooms are mentioned. The text is about the distribution (or better allocation?) of workrooms to the staff of a university.
Edit: Please feel free to correct any mistakes in my text above as I am highly interested in learning english as well as possible (: