Once you reach the drive-in, the Mercer Safehouse quest and the Taking Point: Starlight Drive-in quest (that you received from Preston Garvey earlier in the game) will run in tandem - assuming you haven't completed the latter already. Approach the large blue movie screen then slip through the fence to access the car-strewn parking lot. Call up your Pip-Boy map and fast travel to Lexington, following the objective marker north on your arrival. Your next destination is the Starlight Drive-in, just north of Lexington.
Leave Railroad HQ, backtrack through the crypt and make your way outside. Secure Starlight Drive-In and then use the workshop