Armstrong wasn't able to land exactly in the designated landing location, as far as I know it was too rocky. So he had to fly a bit farther to find a suitable spot. But how much farther from the designated location did he land? A few hundred meters? A few kilometers?
The distance is noted in Apollo by the Numbers.
22,500 feet, that is 6.858 km or 3.7 nautical miles or 4.26 statute miles.
From the Apollo 11 Summary, link from called2voyage:
The 756.39-second powered descent engine burn was initiated at 102:33:05.01. The time was as planned, but the position at which powered descent initiation occurred was about 4 n mi farther downrange than expected. This resulted in the landing point being shifted downrange about 4 n mi.
The LM was maneuvered manually 1,100 feet down range from the preplanned landing point during the final 2.5 minutes of descent.
So about 4 nautical miles of the shift was caused by a lunar orbit error and 1100 feet by the manual maneuver to a suitable landing point.
Eagle was already 3 miles downrange from the expected position at the start of descent, due to residual pressure in the docking tunnel pushing the spacecraft apart when they undocked.
Final touchdown was about 4 miles downrange from the intended landing site:
104:15:13 Duke: Roger. Understand. Omni Charlie. Mike, be advised we have an update for you on the P22 for the LM. We estimate he landed about 4 miles downrange. Your T1 times are updated and your T2, if you're ready to copy. Over.
Assuming that the automated descent didn't do anything in particular to correct for the initial 3 mile downrange error, that would suggest that Armstrong contributed an extra mile or so of downrange distance looking for a landing site.
Based on the maps and the numbers, here's my best estimate of the answer. Using this high-resolution map of the target ellipses, the near precise map coordinates to the landing site are J 6.5 (left to right),7.52 (bottom-up). The squares are each a square kilometer in size, with the desired landing point centered at point L 0,13. Subtracting from the center point, you get that Apollo 11 landed 6.5 km beyond (downrange), and 2.8 km to the left/south (cross-range) of the target point. Using Pythagoras, we get that Neil and Buzz landed 7,077.42 meters off the intended landing site, or 23,219 feet, 10.9 inches if you use imperial, 26.3 degrees off the orbital inclination. Fairly close to the reported offset of 22,500 ft/6,858 m in the reference books.