Fair warning, I only liked the first part of Seveneves; I thought the second part was stupid. You'll get a lot of recommendations for Liu Cixin's "Three Body Problem" which I personally hate (though the first part of the first book is very well written), but if you like all of Seveneves then it might suit you.
My personal favourites that might not already be on everyone else's lists:
Fiasco - Stanisław Lem
This is how you lose the time war - Amal El-Mohtar and Max Gladstone
Feersum Endjinn - Iain Banks
The Dark Side of the Sun - Terry Pratchett (yes, that one)
I loved all of Seveneves, and hate Three Body Problem.
The biggest difference in theme being, optimism that humanity can overcome any obstacle and flourish.
If you want more in that vein, see:
Have you read other non-American/non-Western Scifi?
It's not a universal assumption that the future is good and technology will make us better. I love Soviet sci-fi for the completely different perspective.
Feersum Endjinn isn't a culture novel, so "other" doesn't really apply. I like the rest of his works, but this is my actual favourite of his SF genre stuff. Plus it's relatively short and self-contained which is often a plus for someone new to an author.
Of the Culture novels, my favourite is Excession - but I can't see it appealing to someone who hasn't already read any of the others.
My personal favourites that might not already be on everyone else's lists:
Fiasco - Stanisław Lem
This is how you lose the time war - Amal El-Mohtar and Max Gladstone
Feersum Endjinn - Iain Banks
The Dark Side of the Sun - Terry Pratchett (yes, that one)
Blindsight - Peter Watts
Bloom - Wil McCarthy
Good luck!