According to the 5-foot contours on the King County GIS iMap website, the highest point on Capitol Hill is just south of Volunteer Park and the observations tower. There are two square-shaped 455-foot contours on the west side of the two blocks bounded by 14th, 15th, Prospect, and Aloha. These areas are almost entirely on private property (residences).
That said, all the land in this vicinity is altered by man over the course of the past century or more, so there is no natural ground left. And the area is largely flat. It is hard to deny as ascent of Capitol Hill to anyone who has been to the tower. To be sure, one could walk south on 14th Avenue and east on Ward, probing for accessible higher ground.