No. “That” does not replace “where”. You could say …" there are nice big desks that look like a good place to work" or … “there are nice big desks on/upon which I can work.” What sounds the best is the original phrase, “where I can work.”
“desks that I can work” make “work” transitive on the object “desks”. I.e., you do some kind of work directed at the desks themselves. Exactly what that would mean, I don’t know, but that’s what comes from the grammar. So it’s not what you want to say in this example. Other examples of this construct:
There are many big jobs that I work.
There are nice big planes that I fly.
There are nice big cookies that I eat.