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 ho…
Feersum Endjinn is great, but would recommend starting with other culture novels first.
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.