You can pick just about any day of the season and find hitting streaks that began or ended on that date.  I've catalogued over 600 separate hitting streaks of 20+ games.  Three streaks ended on a July 10, but, interestingly, none have ever begun on July 10:

Ty Cobb, 23 games, began 6/16/1912 and ended 7/10/1912
Roberto Clemente, 20 games, began 6/23/1965 and ended on 7/10/1965
Edgardo Alfonzo, 20 games, began 6/10/1997 and ended on 7/10/1997

The earliest in a season that a 20+ game hitting streak was started was April 7, done twice:
Steve Garvey, 21 games, began 4/7/1978 and ended 5/2/1978
Danny Bautista, 21 games, began 4/7/2004 and ended 4/30/2004

And the latest in a season that a 20+ game hitting streak was started was October 5:
Sam Rice, 30 games, began 10/5/1929 and ended 5/17/1930.

...but Rice's streak was only for the last 2 games of 1929, and then the first 28 games of 1930.  The latest that a streak began in which the batter had at least 20 games before the season ended was Sept 10, done four times:

Pete Browning, 24 games, began 9/10/1887 and ended 10/9/1887
Barry Larkin, 23 games, began 9/10/1988 and ended 4/5/1989 (21 games to end 1988 and 2 games to begin 1989)
Bobby Bonilla, 22 games, began 9/10/1995 and ended 4/3/1996 (20 games to end 1995, 2 games to begin 1996)
Nomar Garciaparra, 21 games, began 9/10/2000 and ended 7/29/2001 (20 games to end 2000 and 1 game to begin 2001).



A Century of Cobb
Ty Cobb's batting line from 100 years ago:
July 10, 1907: at home vs. NY; 3-for-5 with a triple; opposing starter: Newton.  This was the 19th game of a 22-game hitting streak for Cobb, which lasted from 6/22-7/13/1907.