- Short answer - Pretty close, within a few hundred feet. The Tagging of Pacific Predators (TOPP) program has been tracking white sharks since 2000 and has found them quite close to shore, such as beneath the Golden Gate Bridge. Although the question mentions a shark attack on the eastern US, the behavior of Pacific white sharks to those in the Atlantic are probably very similar.
- Longer answer- Research on Pacific white sharks (which are a genetically distinct population) has shown that they are coming closer to shore than previously thought, and spending more time there. They are feeding on seals and sea lions and so will come close to shore for hunting. Using acoustic tags and listening stations, which pick up the unique acoustic signal of a tag within 250 meters, they have been able to track white sharks movement along the California coast. With an estimated population of only about 200 white sharks in the Pacific, it could be possible to tag many of them, then have acoustic listening stations at popular beaches, and alert beach goers if a shark came close to shore. Pacific white sharks also exhibit a pattern of movement, with white sharks mostly completely absent from North America from mid-April to mid-July. This research is all covered on an upcoming episode of Discovery Channel's Shark Week, called The Great White Highway, airing August 16. In about a week, Barb Block (Stanford) and others are releasing an iPhone app to track white sharks in real time (called Shark Net, I think). http://www.topp.org/species/white_shark/
This white shark has two tags, an acoustic tag (front) and satellite tag (back). The acoustic tag can be picked up by a receiver if the shark passes within 250 meters. The satellite tag collects data on location, depth, and temperature. Once the tag 'pops up,' it can be retrieved ($1000 reward if you find one on a beach!) and the data downloaded.
Cite: Jorgensen, S. J. et al. 2010 Philopatry and migration of Pacific white sharks. Proc. R. Soc. B 277,679 - 688. (doi:10.1098/rspb.2009.1155)More questions on Marine Biology: