How to tag a canteen/refectory?

I see your problem - none of the tags seems to be sufficient. And it is not only problem of university canteents. There are self-service restaurants in many office buildings as well.
If the place in question serves regular solid meals (not only snacks or fast-food) I would tag it as restaurant (even if it is self-service). The level of restaurants ranges from simple rural restaurants to Michelin star awarded fine dining places anyway - why not self service school canteen. If the place serves coffee and snacks, tag it cafe.
And if it is fast food tag it as such. In my university there were all three types...

how about a cafe? It serves not only coffee, but also some snacks, like sandwiches and cakes. Fast Food could also be an option... you get your food over the counter and usually a canteen in a university is designed to serve people in short times. They might only have 30 min between lectures. As I understand, fast food on OSM is not limited to Chains like McD & co.

Try looking at these: http://wiki.openstreetmap.org/wiki/Tag:amenity%3Dcafe http://wiki.openstreetmap.org/wiki/Tag:cuisine%3Dcoffee_shop http://wiki.openstreetmap.org/wiki/Tag:amenity%3Dfast_food

Although, may I add another question: Is the uni canteen open for public? I.e., if I go there as a tourist, can I eat there? Even if I am not a member of this university?

If no, then maybe also tag it as access=private http://wiki.openstreetmap.org/wiki/Access

Different countries, different approaches. In Austria, for example, everyone can enter the university and use the facilities like Café, Mensa, library, yes, even listen to lectures. When I was in Paris, the guards didn't even let me enter the university building without a student's or staff ID.