Time Travelers Never Die is about a science fiction writer named Jack McDevitt who's read a bunch of historical biographies and decides to write a novel that incorporates them all, even though there's no rhyme or reason why a time traveler would pick these random points in history.
The "story" begins with David attending his friend Shel's funeral, only to find, upon returning home, that Shel is waiting for him. Shel and Dave are time travelers, so the fact that they die at some point in time doesn't mean much as long as they avoid going to that point in time.
We then get the obligatory flashback to explain how they became time travelers, and eventually learn how Shel died. Shel's dad, Michael, actually invented the time machine, building it into an iPod -- er, sorry, "qPod". When Michael doesn't show up for dinner with his son, Shel goes over to his house and finds it empty. The police are no help, but Shadowy Government Agents show an interest in Michael's disappearance.
Shel gets a hold of some of his dad time machines and, after figuring out how they work, goes back to find out what happens. Dad gives a big infodump, explaining that this storyverse uses a completely deterministic model of time travel, so anything that will have happened has had happened already and we're just not aware of it. If a time traveler attempts to change anything, he'll either suffer a heart attack or his machine will malfunction and dump him somewhere "safe" for the timeline. Thus Shel's very act of going back to warn his father creates a causality loop that prevents his father from showing up.
Dad says not to worry, he'll just make a note to skip ahead in time and show up after Shel went back to warn him. But first he's going to go through with his plans to tour history.
Shel returns to his home-time, but his dad never shows up. Deciding that his father must've gone back to visit his hero, Galileo, Shel recruits his friend Dave, who knows Italian, to help him out. But Galileo turns out to be a dead end. So they try the civil rights march in Selma, which Michael had also expressed an interest in. When that doesn't work, they try the Library of Alexandria, and this and that and the other place. Eventually time travel becomes as much a hobby to them as a quest.
There's really not much of a plot here. McDevitt might as well have thrown in some musical numbers and Dorothy Lamour and called the book The Road to Alexandria. Occasionally one of the travelers will get in trouble with the locals and the other fellow will have to come to his rescue using the Bill and Ted theory of temporal mechanics -- i.e., if you want to get into a locked room, just promise yourself that once you're inside, you'll go back ten minutes and unlock the door.
Some of these adventures are interesting, but their accumulation doesn't add up to a plot. Even the search for Shel's dad comes off as a threadbare MacGuffin, and the explanation for Shel's death is just an excuse for a Bill and Ted style heist wrapped up in a big timey-wimey ball.
The other major problem with the book is that it's like that joke in The Hitchhiker's Guide to the Galaxy about how time travel has made all times the same. People in Renaissance Italy and ancient Greece don't even seem like foreigners, much less people from pre-modern societies -- in fact, they come across as more modern than the redneck yahoos in Selma, who are the only characters who seem historically realistic. Shel and Dave make little attempt to blend in on their travels apart from learning languages -- which they do preposterously fast, even with dead languages -- but people just accept that they're travelers from distant lands. When Shel shows people a photo of his father, they just say, "Wow, I've never seen a portrait like that! What is it?" And Shel explains that it's some new technique from his land, which satisfies everyone. He even flashes his qPod around a few times without consequences.
Overall, the book's a quick, short read, never boring, yet nowhere near as interesting as the premise should be.