Pennsylvania Ballet was started by Balanchine protegee Barbara Weisenberger -- not all of the Children of Balanchine were among his most famous dancers -- and was lead by Robert Weiss for almost a decade. Christopher d'Amboise was AD at Pennsylvania Ballet before Roy Kaiser. Kaiser is a "cousin" in that he was SAB-trained, and his dancing brothers were at NYCB and other companies. The only non-Balanchine AD for the company was Benjamin Harkavy.
In the same time frame, E. Virginia Williams founded Boston Ballet, and Balanchine was instrumental in helping the company by giving her his ballets. Another Balanchine dancer who ran the company was Violette Verdy. Nissinen's was influenced through his tenure at San Francisco Ballet under Tomasson.
Kansas City Ballet's AD was Todd Bolender starting a few years after it was founded until the mid-90's.
San Francisco Ballet was founded by the Christensen brothers. I think Lew Christensen's chapter in Barbara Newman's "Striking a Balance" shows how much Balanchine influenced Christensen.
William Christensen founded Ballet West.
I know there was a Balanchine protege who ran a company in Switzerland, but I can't remember her name. Edited to Add: Patricia Neary, at Geneva Ballet. Neary has also been Assistant AD of Berlin Ballet and was AD of the Zurich Ballet and La Scala Ballet.
More current artistic directors:
- Ib Andersen-Ballet Arizona
- Robert Weiss-Carolina Ballet
- Daniel Duell-Ballet Chicago
- Suzanne Farrell-Suzanne Farrell Ballet
- Nanette Glushak-Ballet Toulouse. (She was also AD of Fort Worth Ballet.)
- Jean-Pierre Bonnefoux (AD) and Patricia McBride (Assistant AD)-North Carolina Dance Theatre
- Colleen Neary (co-AD)-Los Angeles Ballet
- Gen Horiuchi-St. Louis Ballet. Balanchine picked him, but didn't work with him much.
- Christopher Stowell was AD of Oregon Ballet Theatre through the end of last year; his parents were Francia Russell and Kent Stowell, and he went through the ranks at San Francisco Ballet as a dancer.
- Nikolaj Hubbe-Royal Danish Ballet (career under Martins, but greatly influenced by the Balanchine rep)