The historic Capri theater in Jackson's Fondren neighborhood is a cool spot to catch a movie while eating dinner. Or if you're in the mood for bowling, Highball Lanes (located right next door) is a great place for bowling AND dinner. Just make sure you get reservations!
The URL should show you right where the Overlook is. Or just navigate to the Natchez Trace Parkway in Ridgeland, head east, and look for the sign for the Overlook! The multi-use trail starts at the Overlook and goes for 10 miles. It's a great place for a walk!