A real close City of Mount Vernon park, but on the wild and woodsy side. Just on the southeast end of the city limits. Drive to the top for two spectacular views; one to the south and west and the other to the north looking over the city proper. Many trails thread their way up, down and along this ‘Little Mountain.’ Some of the trails are for hikers only, others are also mountain bike permitted. The map gives more information.
See map below to get there from Highland Garden House Bed and Breakfast. Google says it is only 4 miles and only takes 12 minutes, but I think a bit longer in time: