@ChilledChaos
1. The best way to hide is to use the full size of the map. Without going into the actual probabilities, the natural dispersion of the players across the map and the render distance of 5 (6?) greatly thins out the potential for repeated footsteps and eyes across a particular area. Crafty and his staff have put in tools to help cover ground quickly. And now with the Elytras and rockets it's a much easier task.
2. Consider building underground, or at least keep a small aboveground footprint. Also reducing traces of your activities in the area falls in this category, like half-cut trees and the use of cobblestone. Underground bases are invisible to visitors running overhead.
3. Avoid high entity counts. 100 is the limit maintained by staff. But higher than 50 a smart player with F3 debug window up will know theres something worth exploring underground.
4. Avoid oceans. The natural generation of nether portal exits for people traveling out via the Nether roof (a common route on CM) scans for valid locations. If the area all around your base is nothing but water, the only valid location for the portal to generate is your base!
5. Remove your nether portals on both sides. Nether portal mechanics prioritizes active portals to send a player entering/exiting the Nether. When exiting from the Nether the game looks for an existing portal 1024 blocks around the corresponding Overworld coordinates.
6. Consider building in the End or the Nether. Everyone builds in overworld cause that's where most of the cool stuff is. So why not go where no one would bother looking cause no one in their right mind would like living there. Consider using Rule #1 too if you do this.
7. Avoid rare biomes like mesas & ice-spikes. Everyone likes to check out a rare biome.
8. Avoid predictable coordinates, like 50K x 50K. You wouldn't be the first to think to go there.
9. Avoid the world boundaries. Anyone traveling past 12500k in any direction in the Nether gets their coordinates truncated to the world boundary when they go back to the Overworld. That's a high chance of getting explorers delivered to your front door.
10. Kill the cartographer. If you're deciding to use a monument for a base and use a villager cartographer for a map to make it easier, be sure to thank him with a sword to his gut. While cartographers don't give out new map trades to monuments occupied by players longer than 3 minutes, the original cartographer doesn't change his map trade. That means players coming across towns containing the original, "leveled" cartographer, can literally get a map to your base. (This is based on the info I've researched but haven't personally verified yet).
Good Luck!