According to this story, the Republican Party’s choice of Cleveland for the 2016 national convention does not foreclose either a June 27 opening date, or a July 18 opening date.
According to this story, a June 27 opening date might conflict with the National Basketball Association championship games.
A national convention that is held in June gives an opportunity for people unsatisfied with the results of the convention considerable time to support a presidential candidate running outside the two major parties. All but four states have a method for a candidate to get on the ballot for President with a deadline in July, August or September. The four states with earlier deadlines are North Carolina, Texas, New Mexico, and Illinois.