Where would a breton learn magic apart from a court wizard?

Witches, for a start. There's loads of covens and cults in High Rock. If they're more proper and still from a wealthy background, then there are probably plenty of independant wizards and academic institutions for teaching magic in the province without considering the courts and kingdoms. I assume the Breton in question is raised in High Rock - otherwise the possibilities are too many to list. Also, there is a great tradition of magic in all areas of Breton society; it's possible that she or he was simply raised with it around, and took it in naturally.

are there any named institutions in high rock that you know of?

Gwylim University, Llull Popudax School of Old Wisdoms, Kambria Main Campus.

thank you very much

I can't name any besides Gwylim which HQ brought up (which as far as I know, deals mostly with lore and knowledge of a more scholarly and less flashy and magical sort) but the "temple" of Julianos in TES II functions as a http://uesp.net/wiki/Daggerfall:School_of_Julianos - seeing as Julianos is associated with magic as well as logic, education, mathematics and so on, there is probably a good amount of magical teaching in the School of Julianos branches.

But srsly, every Bret lad or lass, between the birds-and-the-bees talk, and the your-mother-and-I-have-been-talking-and-we-think-it's-time-you-moved-on talk, gets sit down by ma and pa and told about the cosmic background radiation that fuels the thaumaturgical expressions of their own inner psycho-asterism.

I may need to hold on to that... With proper credit, of course. It's just too hilarious to let slip by.