Little Bray refers to the area north of the bridge leading to castle street and beyond, it is an older area with a strong community spirit, close to the town and handy for shops etc. My cousin sent her children to the primary school you mentioned and found it very good.
Bray is a great town with lots for families to do. Enquire at the social welfare office beside the train station to find out about the community welfare officer and anything else you will need. check the Bray People Newspaper for local info and rental listings.