The stronghold seems to be really far away from my spawn point, and I end up losing all the 'eye of enders' I have. Any idea on how far a stronghold can be from a spawn point?(Since there can be just 3 in a world, I assume they can be really far away!)
According to the wiki:
All strongholds are located at random positions in a radius between 640 and 1152 blocks from the world's original spawn point, at 0/0 (but may extend further in or out of that area). The three strongholds are spawned at roughly equal angles from the center point of the world (that is, each stronghold is in the region of 120 degrees from the others, measured from the origin).