1. Vacuum Diagrams by Stephen Baxter. When I think of epic hard science fiction, the Xeelee Sequence books spring to mind. With a story line that spans millions of years (and a few dozen books), this collection of short stories is a good introduction to one of the best and most underrated sci-fi series out there. Baxter's Manifold trilogy (Manifold: Space, Manifold: Time and Manifold: Origin) are also fantastic.
2. Foundation by Isaac Asimov. The whole Foundation series is wonderful, but this book is a landmark of sci-fi that should be on any fan's bookcase.
3. The Martian by Andy Weir. This book is what I've been giving the last couple years to people who don't think they like sci-fi. Everyone I've given it to has loved it.
4. Rama by Arthur C. Clarke. Another hard sci-fi staple. The rest of the Rama books he "co-wrote" with Gentry Lee are decent but become more space opera than hard sci-fi. I enjoyed them but many sci-fi fans find them polarizing.
5. Silver Tower by Dale Brown. More of a military thriller than sci-fi (Flight of the Old Dog is another favorite of mine by him) and terribly dated by modern standards (it was written when the Soviet Union was still a thing). But it's the first "adult" sci-fi book I ever read as a kid, so it'll always have a special place for me.
EDIT: Another one:
6. Coyote by Allen Steele. I love stories like this one: primitive, longshot interstellar exploration and primitive, first generation colonization. Especially for desperate reasons. The first two Coyote books were good, but I just can't get into any of the subsequent ones.