Many expat children's activities take place through the school and as most families are away over the summer, there are fewer of the types of activities you mentioned.
If you have already selected the school your child will attend in the fall (if you are not only staying for the summer), you may want to contact the school to see if other children will be staying and/or if the school has a summer program planned.
Some of your choices may depend on the area of the city in which you will be living/staying.
You may also want to contact the American Women's Club to see if they have any members with children your son's age who will be staying over the summer.
For a list of community groups, including AWC, see here:
http://www.korea4expats.com/article-community-groups-clubs-seoul.htmlYou'll find some of the swimming pools in Seoul listed here:
http://www.korea4expats.com/article-swimming-seoul.htmlIf you type 'children' in the search box on the home page of this site, you'll also find pages that provide ideas/suggestions on things to do with your child.
Check out the What's Going On section on this site also -
http://www.korea4expats.com//event.php - the Children & Families section in particular.
Hope some of this helps.
Wishing you and your family an excellent stay in Seoul.