Aliens do make occasional appearances in Asimov's work, but it's true that they're conspicuously absent relative to the rest of the genre. I've long wondered why this might have been. It could be that Asimov wasn't interested in imagining a species without some realistic speculation about their biochemistry (which was after what Asimov's PhD was in). It could also be that he saw what passed for "alien" elsewhere in sf and he didn't want to make the same mistakes. By that I mean, most aliens in written science fiction are the prose equivalent of humans with ridges on their foreheads. To this end, don't be too eager to mock Klingons. An amoeba the size of a mountain that has humanly-comprehensible motivations seems no less ridiculous than an alien with copper-based blood that ended up looking like an elf. At least many of the limitations of TV science fiction come from creators' budgets rather than their brains. Gregory Benford said that rendering the alien is the holy grail of science fiction, so maybe Asimov recognized it for the feat it was, and chose (logically) to expend his efforts elsewhere. I can't claim to feel robbed of the fruits of his talent as a result.
Possibly, whatever questions science fiction authors are exploring with aliens weren't questions that interested Asimov. (Assuming the alien is being used to explore any questions; having them in the story just as mind candy is still a legitimate use of aliens as a literary device, assuming they're actually cool.) Although there is clear technical problem-solving in Asimov's story as Wimmer pointed out (e.g. how to find our solar system from the center of the galaxy), I would argue that Asimov's chief concerns are the interplay between history, psychology, logic and morality. Yes, morality. In adulthood, I have a much greater appreciation for the Three Laws as a vehicle for the discussion of moral dilemmas than I did when I read the books in my mid-teens, and in the intervening years I've also wondered to what extent the atheist Asimov was influenced by an upbringing with the explicit moral dicta of Judaism. (Wondered, because I don't know if he was raised religious or in a predominantly secular community.)
Foundation and Earth is not a "dead end" for the Foundation series. A writer in a corner doesn't draw attention to the corner. To be clear, I'm not making one of those irritating arguments that central figures in literary canons can do no wrong, and that therefore when we find problems in their work, they must just be some clever device or game that we philistines can't appreciate. Asimov no doubt missed points here and there, but this isn't one of them. I'm going to requote the closing lines of Foundation and Earth, as Wimmer and Wilkins did:
"In all human history, no other intelligence has impinged on us, to our knowledge. This need only continue a few more centuries, perhaps a little more than one ten thousandth of the time civilization has already existed, and we will be safe. After all," and here Trevize felt a sudden twinge of trouble, which he forced himself to disregard, "it is not as though we had the enemy already here among us."
And he did not look down to meet the brooding eyes of Fallom — hermaphroditic, transductive, different — as they rested unfathomably, on him.
How could he possibly have drawn more attention to this ending? This passage has resonated in my mind for over two decades now. By announcing this so deliberately, I think he was quite explicitly leaving the way open for future works that would take place after Foundation and Earth. Asimov respects his readers enough to assume they're paying attention and know what he's up to. An excellent example is the change in tone, particularly with regard to sex, between his 1957 The Naked Sun (1956) and The Robots of Dawn (1983). Of course, a major cultural shift had taken place in the real world in the years that elapsed between the two publications, and the books reflected that - to the point where an event in the first novel was explicitly reinterpreted in the second novel as an orgasm! The discussions between Lije Bailey and Gladia Delmarre on this matter highlight to some extent why this should be so, but even without this, it's obvious to even the most tone-deaf reader that the emergence of sex as an Asimov theme had more to do with contemporary changes in the real history of twentieth century Earth than with any revolution in Spacer culture. As before, the alternatives are that either a) Isaac Asimov didn't know what he was doing, or b) that he knew exactly what he was doing and why, and assumed you would too. It also bears pointing out that option (b) is more in keeping with Asimov's famously transparent prose.
Above: Janov Pelorat, shortly before his famed discovery of humanity's homeworld in the Sol system.
Why is there an early- and latter-day Asimov? Wimmer and Wilkins also make a comment about the difference between early and late Asimov; one of the stylistic differences is his interest in sexuality as discussed above. But this raises the question that there's a big gap in Asimov's fiction-writing in the 1960s and 70s; in his biography he even commented that at the time he feared his writing career was over and described the stylistic changes that overtook the genre as "un-Asimovian". Has anyone ever done a graphic presentation of Asimov's prodigious output? (Hint hint. Someone else do it. Not me.)
The two best works from the Foundation universe that you haven't read: Psychohistorical Crisis and The Currents of Space. Yes, Psychohistorical Crisis is apocryphal to the canon, but it's an outstanding work in its own right, discussed more at length here. The Currents of Space is a proto-Imperial-era work which manipulates setting to turn a familiar injustice on its head, and here dark-skinned people are oppressing light-skinned people. In the 1950s this may have been a more striking work than today, but it's still pleasant to see someone using setting-manipulation for allegorical ends in the genre that's best-suited for exactly that. If your genre allows you to change most of the elements of literature from constants into variables and you don't do it (consciously or otherwise) then you're just going through the motions. Asimov certainly was not.
Of interest: The real-life Hari Seldon? Peter Turchin's work is worth a look; He even has a book with math specifically about the fall of empires. If he is suddenly exiled to Easter Island and starts a university there, start worrying.