May I recommend that if you're an Asimov fan, you read Psychohistorical Crisis. It is a non-authorized addition to the Foundation series, taking place two millennia after Hari Seldon. While the names are different, the universe is recognizably that of the Foundation series. And the novel succeeds not only as a Foundation tribute novel but as an outstanding work of science fiction its own right. (Here are two reviews.) What's so great about it?
1) It knits together history so far with distant future history in a non-childish, non-current-era-centric way. This is rarely done and is the holy grail of projection fiction; when it is done it's usually done in a narrow way around a specific theme or technology. Reading Kingsbury feels like reading history.
2) There's also some really interesting hard science/philosophical speculation woven into this book, as there usually is in Kingsbury's work. One discussion involves the finite information density of the universe and how that necessarily means that history is lost, not just in the sense of destroyed documents but the basic physical recoverability of information about past events.
3) He introduces a technology called the "fam" to deal with the complexities of a culture that has endured and accumulated (and lost knowledge) over tens of thousands of a years. The fam is a neurologically-interface computer that allows people in the novel to deal with, among other things, the galaxy's ten million word vocabulary, negotiate financial transactions and human geography, and in general function. Kingsbury thinks about the technology in depth. Removal or loss of the fam has devastating consequences that parallel brain damage in our own culture, losing the ability even to navigate ones neighborhood or understand language. Still there are exceptions. One character takes off his fam to stroll meditatively through nature, and another invites a sex partner to try intercourse without it, to focus on the bestial sensory world unpolluted by semantic thought. The massively complex, nonsystematic accretion of culture is terrifying to contemplate, and the only better metaphor I've run across is from a William Gibson novel, when a character observes a repair job in the London subway and notices how many unknown layers of tile there are on the walls, in a kind of cultural atherosclerosis.
4) It's interesting watching for Kingsbury's workarounds so that he could (legally) play in a universe that didn't necessarily want to be played in. Apparently there was no legal action from the Asimov estate but there were threats. Unfortunate, since the Asimov canon would be poorer without this apocryphal contribution.
5) This essay isn't the first to observe that science fiction is a genre which seems to assume (on average) that in the future, all humans will be white heterosexual male anglophone agnostic physical scientists or engineers. This has changed for the better over the years but when this assumption is violated it's still comment-worthy. (Case in point, the role of religion in Dune or the Pitch Black series.) This doesn't damage science fiction to the point of uselessness, but the values of its authors are more necessarily manifested, because they're often consciously writing about today's trends projected further into the future. Another interesting subject here is Iain Banks, whose Culture is basically the Enlightenment writ large, though his writing seems quite conscious of this idea, and the other concepts the Culture conflicts with are his foils (the Hells, the Affront, and the "out of context" problem.) In fact an argument can be made that, in having the protagonists use astrology to subvert psychohistory (the near-dictatorial guardians of which are some the most enlightened humans ever to live), Kingsbury is making a comment on the limits of reason and the Enlightenment to alleviate the human condition. A comment about salvation through Christ in the historical timeline Kingsbury included with the novel might lead one to interpret this as motivated by theism.
Consequently what I like about Kingsbury's future is that it's not obviously Western-centric and unquestioningly extending the Enlightenment, both of which assumptions are still the implicitly the case (generally) in science fiction. Kingsbury does actually mention America by name as a flash-in-the-pan empire - in naming past nations Kingsbury's history is more clearly a future history of the actual Earth than Asimov's was (or perhaps could have been, since in the Foundation era in the canonical Asimov universe, Earth had been forgotten as the human homeworld.) This distant future's cultural conventions are less familiar to a modern Westerner than in Asimov's series. There are a lot of interesting changes between the first three Foundation novels and the much later last two, driven by cultural changes in the intervening era, although to his credit Asimov addressed many of these directly. In Prelude to Foundation he addresses the racial makeup of the characters for the first time; Westerners, Easterners and Southerners parallel modern white, Asian, and black humans. Of course Asimov is not alone in this. As has been observed of Star Trek, this either supposes that off-Earth settlement will begin in our relatively near future, or more sadly assumes that humans of varying ethnicities will never mingle genes. (It's more annoying in Star Trek. It's 2300 and most people on Earth are still of one or another distinct race? Really? Depressing. Don't tell us you couldn't find multiracial actors either, it didn't seem to be a problem for Fifth Element.)