Yeshivat Netiv Aryeh is right there too. You actually must enter the kotel plaza to get into it, on the stairs next to where the old police station was (there is an excavation there now). Lots of shiurim there in english.
There is also Yeshivat Hakotel in the upper Rova. There is also Yeshivat Birkas Hatorah for balei teshuva, I’m sure they have english shiurim… on Rechov Ohr Hachaim next to the Heritage house.
Any other specific questions about the old city? I lived there a few years.