Recently, I got a call from a mother whose son wants to learn about computer programming. His school offers classes but they don't start until the fifth grade and they won't make an exception for her son who will be a third grader in the fall (seven years old). I found two summer day camps in the Cincinnati, Ohio area that have camps for third graders. (Note: The summer camp folks look at the grade your child will be in in the fall.)
I don't know much about these camps and this is not a specific recommendation. The main reason I'm posting this is to reassure parents that seven years old is not too early to begin learning about computers, whether it's developing games or writing programs.
One set of camps are offered by Classroom Antics. The camps range from Junior Video Game Design (ages 7 to 9) to Stop Motion Animation (ages 9 to 13).
Another place for a variety of scientific camps, including programming camps, is CINSAM at Northern Kentucky University.
Drake Planetarium also has camps that involve concepts related to programming. Once you display the page, click on "2015 Summer Camps" for more information.
There may be more camps that I'm not aware of. If you are connected with a summer computer camp, drop me a line and I will update this post.
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Updated May 17: Added Drake Planetarium.