Country Day School? Not sure when they start though.

Headfirst has one in Oakton and is generally well reputed. Fairfax county also has a few camps those early weeks (like at Spring Hill rec center). Brooksfield starts early but is hard to get in if you're not in their afterschool program or a returning camper.

You can do a couple of weeks at Knights of Columbus Camp in Arlington. Their first session starts June 10th.
https://arlingtonknights.org/camp-session-dates

Last day of the current preschool is May 24th. Already booked one music program starts from June 24th. but there are these 4 weeks gap in between.

so I am wondering if there is any camp that is available in the first few weeks of June? sport, art, or daycare program or anything else.. Thanks