BLS is considered a little better than BLA, but they re both testing schools. Other Boston Public Schools in general are not good. Another option you might consider is living in a nearby suburb, such as Brookline or Newton. Both have excellent school systems, and are very close to the city (Brookline especially). You can get to Boston from both towns very easily on the T. If cost of living is a concern, Newton tends to be quite expensive, but there are some cheaper places in certain areas of Brookline, if you look hard. Good luck!
Please see: http://www.bostonpublicschools.org/node/�� As you can see, there are more than a handful of high schools in Boston, and that many are specialty schools featuring, music, engineering, business, the sciences, etc. The website is informative and easy to navigate.
Latin Academy and Latin School are good schools, but you have to take the ISEE to get to them. They atre pretty much the only public schools in Boston