Technically it's slightly lower surprisingly early in the trip -- get to an altitiude of 500km and g is down to about 8.5m/s, at 2000km it's 5.7, and by the time you get just 1/10th of the way it's pretty much gone. At some point the moon's gravity will start to work with you and pull you in.
According to Wikipedia [1], Gordon Pirie ran 347,600 km in the 40 years to 1981. He lived another 10 years after that, so he might have come close. The distance to the moon is 384,400 km.
My girlfriend does about 300,000' of vertical gain a year which I think is the altitude that's considered the edge of space :)