The two parking options are the Bryan Center and the Science Drive Garage (next to the JB Duke Hotel). The Bryan Center is closer to Gross Hall. Both charge $2/hour with a daily max of $12. They are the top two options on this page
A new bus schedule (for the CCX: Central Campus Express bus, form East campus to West campus) starts on Monday. For those staying within walking distance of East Campus, you can board the bus at the East Campus Quad and ride to West campus. When you arrive at West Campus, you will see the Duke Chapel from the bus stop. Walk behind the chapel and continue through the wooded area – after this wooded area you will arrive at Science Drive. Cross the street, turn left, and walk south along Science Drive for about 200 yards – you will find Gross Hall on the right, just after you pass the camel statue (the building is offset from the road, behind trees).
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The Bull City Connector is a free city bus service that is a convenient way to go between West Campus and the downtown area, where there are many restaurants and hotels and things to do in the evening. Here is the service map for this bus.