To my ears, both are fine, grammatically, although I prefer the first, with the singular "destination". I'm sure there's a technical reason as to why the singular "destination" is permitted with the apparently plural "Dying professors" but maybe I'm just saying that 'cos I like it better! Even if there is such a reason, I'll have to leave it to someone smarter to explain. All I know is, as I say, they're both fine to my ears. Grammatically.
But I do have a problem with your metaphor itself. What exactly does it mean to refer to professors as a destination (or destinations)?
Typically, "destination" means something like the endpoint of a journey, so sure, in some sense you travel to meet the old dude, and so he is your "destination". But without any further context, I find that word choice confusing, or at least unhelpful; not worth the metaphorical effort, as it were. The reason I even mention this, tangential to your question though it may be, is because when trying to answer your question about the correct plurality I found myself dissatisfied with either form. Then I realized what was throwing me wasn't the plurality, but the metaphor. So, change the metaphor and maybe your plurality question will just go away. 🙂