Reccomend a book by CJ Cerryh and/or Poul Anderson.

For Cherryh you can't go wrong with Downbelow Station or The Faded Sun trilogy. With Anderson there's obviously Tau Zero and The High Crusade. There are too many for both authors to recommend without knowing what sort of story you're looking for.
That's almost exactly what I would have said. While The High Crusade is excellent, I'd have said Brain Wave. And a lot of people do love the Chanur series (which I also like). But it's hard to find a bad Anderson (though there are plenty of "just" proficient ones) and the only one of Cherryh's first zillion books I'd recommend avoiding is Hestia.
The Broken Sword by Anderson is pretty dark and fascinating.

There's a bookstore nearby with several Cherryh books. I may try one, I've never read her before.
What Vince and J-Sun said.

I’d add for Anderson, Boat of a Million Years (best SF novel of immortality I’ve read), and for Cherryh, you also won’t go wrong with the Morgaine books.

But the initial suggestions are fine.
The Broken Sword by Poul Anderson
Conan The Liberator by Poul Anderson
Ending Flandry by Poul Anderson

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