A bit more than 250 miles out. The planes themselves actually were detected by radar, but were initially misidentified as being a squadron of US bombers returning to base. Keep in mind that the radar they had in operation then was incredibly crude even compared to the radar equipment they would be using even a year or two later during the war. The first wave of Japanese planes shot down American planes as they encountered them, and took the defenders by enough surprise that none of them managed to successfully get off a warning by radio.

Additionally, because the US was not currently at war with anyone they were not operating air patrols to spot for enemy ship activity in the vicinity to a degree sufficient to ensure spotting them in advance (such operations are very costly of resources and pilot time).

Interestingly, if there had been a rash of rumors of a possible enemy attack on Pearl Harbor around that time the results might have been a little different. The pilots might have been more on the ball in clueing in to the attack and reporting it, the radar operators might have noticed something odd and started an investigation much earlier, anti-aircraft weapons might have been manned, ammunition might have been at hand rather than locked away, etc. The Americans really were caught disastrously off guard.

Interestingly, an unknown sub's periscope was spotted by a destroyer early on the morning of the attack but nobody was expected an all out air raid so it didn't cause the level of immediate alarm it probably should have. By the time the sub was engaged by the destroyer the air attack was already underway.

The first unambiguous knowledge of an attack by upper echelon command did not come until after bombs and torpedoes had already been launched towards ships in the harbor. It was only 15 minutes between the first call that an air raid was happening and the Arizona being blown up.