We don't know what the Thing's plans were, and it is unlikely that Carpenter ever considered the issue. There is no information for us to work with in the Carpenter film.
The Prequel (The Thing ):
The script for the prequel, however, makes it clear that the Thing ended up on earth totally unintentionally. The prequel script's explanation of the spaceship crash we see in the opening sequence of Carpenter's movie is as follows:
An alien race is flying around the galaxy (or maybe beyond the galaxy), apparently collecting specimens of other life forms. The ship's crew inadvertently collects a Thing, presumably while it is in the form of some other species. The Thing breaks loose and begins to assimilate the ship's crew. The last remaining member of the crew, now fully aware of how dangerous the Thing is, decides to sacrifice itself to kill the Thing, and deliberately crashes the spaceship into the nearest available planet. Unfortunately for us, that planet happens to be the earth. Whether the ship's pilot made an active choice to crash in the least inhabited part of the planet (i.e., Antarctica) is not clear, but that is precisely what happens.
The crash kills the last crew member, but the Thing survives, crawls from the wreckage, and freezes solid in the ice. The Thing, and the spaceship, remain buried in the ice for tens of thousands of years. A Norwegian team of scientists discover both, dig the Thing out of the ice, and bring it back to their camp. It wakes up and all hell breaks loose. One piece of the Thing attempts to restart its spaceship and presumably flee the planet, but it is stopped by two of the Americans in the Norwegian team. One of these Americans has been assimilated, the other American kills it, and then chooses to die in the snow.
The Norwegians are wiped out, except for two men. One piece of the Thing survives, taking the shape of a dog, and flees the ruined camp. The two remaining Norwegians hop into a helicopter and give chase.
John Carpenter's The Thing
The dog-Thing runs to the American Outpost 31, where the erratic behavior of the Norwegians alarms the Americans. A brief gunfight ensues, the Norwegians are killed, and the Dog-Thing is brought into the Outpost.
We all know what happens next: The Dog-Thing assimilates one or two men, they assimilate others, everybody kills each other, and the American Outpost is destroyed, leaving only two of the men alive, although we don't know which, if either of them, are infected.
As the battle was raging, the men discovered that one of their former colleagues, Blair, was assimilated at some point, although we also don't know when this happened. Blair-Thing had been locked up in a tool shed, and had burrowed a cave into the ice below the shed, and proceeded to begin construction of a small flying saucer.
The consensus view of what the flying saucer was intended for seems to be that Blair-Thing wasn't trying to get off the planet, but merely wanted to get away from the men in the Outpost. It wanted to reach a populated area full of unsuspecting victims, because the men in the Outpost were on their guard, on the attack, and incredibly suspicious of each other, including (and especially) Blair. However, this is only a theory, proposed by fans, and cannot be considered canonical.
It didn't make sense for Blair-Thing to stick around in Antarctica, because there are maybe a hundred people living there at any given time. It wanted to infect the entire world, and Antarctica was the worst possible place to begin that process.
Peter Watts' Short Story The Things
In a noncanonical short story, written from the perspective of the Thing, we get far more insight into the Thing's mindset than is available anywhere else. In this story, we learn that the Thing actually considers assimilation to be a desirable outcome, and is shocked to find that humans aren't willing to accept being assimilated. Everywhere else the Thing has been, life forms have been perfectly happy to be assimilated. Earth is a totally different story, and the Thing is genuinely hurt by the hostility humans have shown it.
Here, though nowhere else, we see that the Thing's self-proclaimed mission is to spread the gift of assimilation to every planet it can reach.
John W. Campbell's Novella Who Goes There?:
This story is very similar to the John Carpenter film, aside from a scene (which appears in the script for Carpenter's movie, but was never filmed) in which a Dog-Thing attempts to flee the Outpost and reach the shore of Antarctica. The characters who chase it down are certain that it intends to assimilate an animal, probably a bird, and thereby escape Antarctica without the need for a flying saucer or other vehicle.
In the Carpenter film, the Thing probably didn't plan very far ahead, and after it woke up, it was probably just trying to keep itself alive long enough to assimilate a few people and get the hell out of Antarctica so it could reach a more populated area. One piece of it tried to leave the planet, but it also left another piece behind, possibly to ensure that the rest of the planet would eventually be infected.
Blair-Thing's flying saucer was quite small, and it seems unlikely that it was intended for interplanetary travel. It was probably just supposed to get Blair-Thing to a more suitable location from which to begin the process of global assimilation.
Is the Thing biologically compelled to assimilate other beings? Absolutely. We don't know whether the Thing has a native form, but it certainly seems to be compelled to assimilate everything in the vicinity at the earliest practical time. Is it biologically compelled to infect other worlds? We don't know if it is aware that other worlds exist. I definitely think it knows about the existence of other planets, and it certainly makes sense to say that, at the very least, it knows about all the planets it has already been to.
It is probably safer to say that if and when it finds itself on a new planet, it will inevitably begin to assimilate everything it encounters as quickly as it can safely do so. Assimilation is its rason d'être, so when it gets somewhere, it starts assimilating.