To play old Nick's advocate, "Navigator" might be an anachronistic name for a modern profession, the same way "Records Officer" in "Court Martial" seems to be some sort of a computer wizard who won't be spending any of his valuable time maintaining the ship's records.
That is, rather than find the quickest route from A to B, Chekov might concentrate on monitoring nearby traffic, adjusting the navigational deflector to balance protection-of-ship vs. drag-induced-by-deflection, or running the sensors that tell where A and B are in the first place. Or whatever.
Just about the only insight we get into Chekov's line of work is the instance or two when he's told to "calculate a spiral course" or "lay in a parabolic course". But even there, it seems the choice is made by the CO, and Chekov (or sometimes Sulu, directly) just punches it in - his role above and beyond feeding the automation with the skipper's command is still a mystery.
Interesting observation, considering the NX-01 didn't have a navigator stationed on the bridge and there was a whole lot more unknown about space travel at that point (considering they had to borrow maps from the Vulcans).
Based on what we saw though the run of TOS, the navigator seemed to spend much more time coordinating battle drills and making star charts (The Corbomite Maneuver), as well a serving as a weapons officer (Journey to Bable). Maybe the navigator serves more as a watch or duty officer, and just gets involved with actual navigating when a human can do do a better job than the computer.