The only cafe I know in Oxford is Greens which is next to the Bird and Baby in St Giles, is nice, if pricey, but has accessibility issues.
I think in the specific case of Oxford (and probably more generally) I am pretty confident it would be possible to find a nice café (although not all will have wheelchair access). Off the top of my head, the Turl Street Kitchen is nice (if a bit trendy) and G&D's (St Aldates) would give the meetup a different vibe. Participants would be under a bit more pressure to order *something* (Wetherspoons being very lax about this) but in those two cases I've never had trouble.
Possibly university, community, religious or GLAM space might be used especially if an additional event was involved, but we would be very lucky to get such a venue on a recurring basis.
Certainly in Oxford it is generally pretty easy for a student to book a room at her/his own college, and many are without cost, although they tend to be more lecture theatres in setup than cafés!
Harry
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