Hello. I live in Cambridge, MA and am from Boston originally. One thing to keep in mind: In order to attend a public school here, you must live in the city/town that you want your child to attend. They are quite strict about this. (I believe that this is different in Ireland.) Brighton, Cambridge and Newton are all different cities, with different school systems. Brighton is part of Boston and would be part of the Boston Public School system. They all have high standards. Boston and Cambridge are more urban, and bigger, so they have problems that can go along with that. Newton is more suburban, but also more expensive. There is a big range of schools in Boston itself. I am not sure how much choice you have in Boston, but in Cambridge, we have our choice of 12 primary schools to try for. It is done by lottery. Newton has very high standards, but I think you have to go to your neighborhood school, no choice. However, I think you would do well in any community.
Private schools are different. Since you pay for them yourself, it does not matter where you live, but they can be harder to get into. There are many private schools in the Greater Boston area. I would do a search on private schools in Eastern Massachusetts maybe. Best of luck!