Bolshoy has National Spanish dance company as a guest in the end of July. You can check the schedule here http://www.bolshoi.ru/en/poster/ But if you want to see Russian ballet it's not the case. Then I suggest you to visit "Stown flower" (July, 26) or "Swan lake" (July, 30) ballets in Stanislavsky and Nemirovich-Danchenko music theater http://www.stanmus.com/schedule.html
Talking about concerts. You should definitely visit annual "Afisha" magazine picnic on the 31st of July in Kolomenskoe estate. You can check the festival program here http://concert.ru/Details.aspx?ActionID=14955 (roll down a bit for the English text). Trendiest place.