Contagion is a hard science fiction story about a world stopping virus, and it got every single social phenomena correct. 

I recently read a book called Artemis, which is very hard sci-fi as far as I can tell. It goes into great detail describing the economics supporting the moon base where the story takes place -- how much money it makes from tourism vs. exporting rocket fuel, how it got started by a corporation under Kenyan flag of convenience, etc. I don't know enough economics to judge whether it succeeded but it certainly tried to get the economics right, and seemed plausible enough to me.

The Mote in God's Eye is a pretty good example of social science fiction in addition to being a great science fiction novel in general.

The Three Body Problem (trilogy) by Liu Cixin is a masterful work that combines thoughtful hard science (the author is an engineer by training) with a keen political and sociological eye. Sociology is actually a core theme of the book, and the author goes so far as to define a "cosmic sociology" (I'm probably forgetting the actually term from the book, it's been a while since I finished reading). I can't recommend this author enough. The story is enthralling, the scientific and sociological predictions are delightful, surprising, and strikingly intuitive at the same time. I wouldn't place it is is merely a great sci-fi epic; it's truly an unparalleled work of literature and imagination.

Well, integrating all our best knowledge of social sciences for SciFi is hard. I am not sure if I can judge if it was successful or not in most cases. What I can point out instead is a couple of works where something like this had been attempted, as the author gave serious thought on how different technology and environment would affect society:

1. Moon Is A Harsh Mistress by Heinlein
   I think the elaboration on how family structure is changed due to low female:male ratio and dangerous environment makes sense ( https://www.reddit.com/r/AskScienceFiction/comments/214z3t/the_moon_is_a_harsh_mistress_how_do_line/ ), and the book contains a lot of good thought on other things like this.
    
2. Revelation Space series by Alastair Reynolds
   In these books a lot of different social structures are listed that are possible due to technology, such as the Democratic Anarchism (quoting from the wiki):
   "The Demarchy functioned by means of a neural implant that constantly sought the user's opinion on aspects of Demarchist life. This constant prompting eventually faded away into the user's neural background, much like the ticking of a clock might fade away into background noise.
   ...
   Each core was tasked with collecting and processing votes, and also determining whether or not the elected decision was the best one in previous elections -- voters who continually made "good" decisions were rewarded by having their vote count for more than one standard vote."
   The second book ("Chasm City") also elaborates on how the crew of a small fleet of multi-generational interstellar ships would live and be organized until they reach their destination in the not-so-far future (so without neural links and magic gadgets).
    
3.  We Are Legion (We Are Bob) by Dennis E. Taylor.
   This one is less rigorous on the "hard" part than the previous two. I really like some ideas, such as if  human minds can be uploaded and multiplied, we would could end up a whole industry being operated by the copies of a single expert.

Depending on what you define as hard SF, the Nexus trilogy by Ramez Naam might fit. I've seen it described as hard SF, as "having some hard scifi elements", and as "dumbed down science fiction" by a particularly displeased Goodreads user; take your pick. I remember it being very easy to read and making more of an effort than usual to consider the society surrounding the characters. That might not mean getting the social sciences exactly right, though.

In general, I think the closer the time period is to our own, the more likely it is that the social sciences will be right, since the author will have more material to base them on. 
It's been some time since I read one of his books and I'm not sure if he counts as hard SF, but maybe Ian McDonald? I remember being impressed by the complexity of River of Gods. If anyone has read more of his books, please confirm or infirm my guess.

Black Mirror?