Not too far away...
@ Jon Green:
You're absolutely right. A non-allied fleet would know that the US Government thinks their sub is within 50 miles of the buoy, so hey, they only have to cover more than 150 square miles of ocean.
50 miles is probably not even close to accurate though. It's probably much more. Ohio class ballistic missile subs cruise at 20 knots*, so if it really was a 50 mile radius, the sub would cross it in less than 5 hours.** So either the range is significantly higher, or they'd drop several buoys, or both, which dramatically increases the area in which an enemy fleet would have to search. Given the stealthiness of US submarines, one could be within a mile of you, and you'd probably never know it. The terms needle and haystack suddenly spring to mind.
* The unclassified speed. Also, Los Angeles class fast-attack subs cruise at 20-25 knots, and Seawolf class subs cruise at 25+ knots. The seawolf has a maximum published speed of 35 knots (40 mph) while submerged.
** Keep in mind a nautical mile (6,076 feet) is longer than a statute mile (5,280 feet)