Salvage and Demolition by Tim Powers
Finding a logically consistent, intelligent, interesting, and serious time travel story is like finding water in the desert. It's not impossible, it's just very rare and a great joy when found. Here is one of those "water in the desert" stories.
Richard Blanzac is a rare books dealer who stumbles across a manuscript in a cardboard box from a 1950s San Francisco poet. It's a translation of an ancient Sumerian text. If you've learned anything about ancient Sumeria from movies, television, and novels, they were a crazy bunch who worshiped the sort of gods that love to mess up the universe. It might be apocalyptic destruction; it might be mass insanity. Any way, it is bad news. Naturally, people are after the manuscript, including some lady in an old-age home who is the legal executor of the poet's estate. She wants it destroyed; others want it for their own nefarious purposes. The big twist hits early when Richard is cast back into 1950s San Francisco where he encounters the young poet. She is also being pestered by cultists for the manuscript but she wants it preserved.
The story has nice twists and turns which keep up the excitement. And, as I say, it is a nicely consistent and smart time travel story that will have you on the edge of your seat. It's very enjoyable as a science fiction story and has interesting characters.
Parental warning: There's a bunch of drinking and smoking (the part in the 1950s), some violence, and one implied sex scene. This isn't for little kids, but teens and older will enjoy it.