The gorgon is an underutilized monster, a good enemy for intermediate-level parties. Thematically, it fits in well alongside golems and other constructs. Yet it’s categorized as a monstrosity, and reading between the lines of the Monster Manual flavor text, it’s evidently meant to be an evolved creature, so it will have the same survival instinct as any other monstrous beast.
Gorgons are high-Strength, high-Constitution brutes, and their Intelligence is animal-level low, so they’re indiscriminate brutes. Their senses are keen, though (Perception +4), so it’s hard to slip past one unnoticed. They feed by petrifying their prey, then smashing it into gravelly Grape-Nuts that it can consume. They’re not evil per se, but they are apex predators, and once they’ve locked on to potential prey, it takes a lot of damage to get them to reconsider their plan.
The gorgon attacks when the distance between itself and its target closes to between 30 and 40 feet. At that moment, it charges forth (movement) and makes a Gore Attack (action), using the Trampling Charge feature to try to knock its target prone. If it succeeds, it gets to strike again with its hooves as a bonus action.
Although its Petrifying Breath feature is powerful, the Trampling Charge feature is better for initiating combat; the gorgon uses its breath weapon primarily to keep its prey from getting away. Read as written, the Trampling Charge feature seems to allow the gorgon to continue to gore and trample a victim as long as it remains prone, so that’s what it will do; only if the target gets back up, or if three or more foes come at it at once, will it use its Petrifying Breath against them. If it uses its breath weapon against multiple creatures, and some are petrified while others aren’t, it will prioritize a target who’s still moving over those who are immobile during its next attack.
Incidentally, the minimum distance for a Trampling Charge is 20 feet. The gorgon’s movement is 40 feet. That means that in a single turn, a gorgon can run 20 feet away from its prey, then turn around and charge it again. In doing so, it may subject itself to one or more opportunity attacks, but a tough, stupid brute like a gorgon won’t care. Plus, a restrained target has disadvantage on its attacks. So when the gorgon has knocked an opponent prone, and that opponent gets back up, it will first use its Petrifying Breath against it, then run 20 feet away, turn around and charge back, in order to try to knock it prone again. (The target doesn’t have disadvantage on the Strength saving throw—the restrained condition only affects Dexterity saves.) It will also perform this maneuver if it’s just tried and failed to knock a target prone in the first place.
A gorgon will retreat when it’s seriously injured (reduced to 45 hp or fewer). It will use its Petrifying Breath, if available, one last time before retreating, then back away at its full movement speed, irrespective of opportunity attacks against it, and Ready a Gore Attack action against any creature that comes within range.