To create the parallel Creative Mode world, click "Play" then "Edit". This is normally the screen where you delete a world, but you will also see all the numerical seed values shown for each world. Write down the number for your world. Then cancel, create a new world, select Creative Mode, click "Advanced", and punch in your seed.
To measure distances, fly up in the air above your starting point, point yourself toward your destination, then fly forward and start a stopwatch at the same time. When you get to your destination, take the time in seconds and multiply by 1.85. This should be a fairly accurate estimate of the number of segments you need to make underground to get to your destination. (Multiply again by 6 if you prefer the distance in meters.)
You can also use this distance measuring method to map out your entire world.
In the example map below, each square represents 20 segments. What started out as a
relatively "boring" world is now very interesting due to our using the parallel
Creative Mode world to find the mesa biome. Because it is so far away, over a period
of a few weeks surface rail transportation was added so there's now a way to collect
resources from the mesa and bring them home efficiently. The new subway being
constructed provides access to more of the mesa as well as some very rich caves.
Eventually it will be extended all the way back to the spawn point; the map is a good
way to plan this route.
(By the way, the map above depicts the same world that the 3-D Pac-Man House and 13 minute surface rail ride loop are in.)
Miscellaneous screenshots: When the tunnel hits a large cave, or the ocean floor: