I dont have firsthand knowledge about the locations but I have experience with both good and bad martial arts education. I just looked at the websites and The Core Fight Academy looks the best. Champion ATA is too flashy and seems to focus on nonfunctional martial arts (karate, Taekwondo ect.). I can't find a website for the third.
Also I would sugest Judo for a 6yr old instead of Jiu Jitsu... Judo is mostly throws and dealing with a standing opponent, while Jiu Jitsu is broken arms and wrestling on the ground. Also Judo is designed to practice said throws on actual opponents in a safe/controlled setting and nothing is better for a kids self estiem than throwing another kid... again in a 100% safe and controlled environment.
Good choice over Karate though because it is not considered a functional martial art... meaning someone trained in Jiu Jitsu can easily defeat a Karate practitioner of equal skill/experience (same goes for wrestling).
Ps.
Lol @ Mandy B.- Jiu Jitsu and Wrestling are very different martial arts. Jiu Jitsu fighters were dominant in the UFC for a while however not terribly so for almost 5 years now
Lol @Dad On purpose- Jiu Jitsu does not include striking, UFC striking is dominated by Muay Thai