I now know the answer to my own question, so I'll share it, in case there are others in my area still wondering.
They will be showing various clips from the show and having discussions and snacks. From someone running the event, it was described to me as "a book club for Doctor Who".
I'm sure the group dynamics will dictate what actually happens, but the intention is for there to be no focus on any particular Doctor or Current/Classic, but to spread the discussions evenly through all.