If you like Burke Lake, try Lake Accotink and Huntley Meadows. Hidden Oaks Nature center is a good spot and has some short trails in the woods. Their playground is pretty basic (should be replaced w/in a year).
Here's some other threads with suggestions
https://www.dcurbanmom.com/jforum/posts/list/265011.page#2837592
https://www.dcurbanmom.com/jforum/posts/list/314318.page#3718368
https://www.dcurbanmom.com/jforum/posts/list/352654.page#4489022