Yes there is a real place called Watership Down. It is a broad, treeless, hill 6 miles south of Newbury; the home town of Richard Adams, who wrote the novel of the same name. Nuthanger Farm, the scene of several lively chapters, is set back from the road and is not sign posted.
To find the site of the rabbits' warren, take the country lane (Ecchinswell Road) which runs south from Ecchinswell and cross over Fox's lane at the cross roads. The lane then climbs up over the western end of Watership Down. Near the top, beyond a grove of trees, a foot track on the left curves across the face of the down, close to where Adams places the warren. You can walk along the track and perhaps catch sight of a rabbit if you're lucky.