The Catholic religion is one of the largest and most deeply rooted faiths in Boise and I have heard that St. Josephs Elementary Catholic school downtown next to the Catherdal is the best of the church ran elementary schools in Boise. This is the word from friends who have children attending this school. Here's the website.
St. Joe's Catholic School - Kindergarten, Elementary, Middle School Education - Boise, Idaho
St. Maries is also supposed to be a great school.
Intro
There are others in Boise outside of downtown but I am not really familier with them. From what I have heard though the vine is that both of the schools I have listed are the best Catholic elementary schools in the city are great alternatives to public school.
Here is the main website which lists all of the Catholic schools in Boise, and the rest of the state.
http://www.catholicidaho.org/