Don't be afraid, some parts of the 8th and 9th district are actually quite nice. I'm sure BonzaiJoe can provide you nice memories from Mester utca

On the other hand, Andi's brother lives near Rákóczi tér. Well, he was only robbed once in the past year.

Generally speaking the 8th district between Üll?i út and the Danuba is safe and sound. Above that not recommended. East from Orczy út you can also live safely.
I think central K?bánya would also be a rational and cheap choice, even if it means a bit more travel for your girl for a year. The Óhegy area of k?bánya has good traffic possibilities and is very clean and well-organized. My mother lived there for 5 years and liked it a lot.
In any case, living on the Pest side after Buda will be strange for sure.
But better move now. End of august all the good&cheap rents will be filled by new students