I don’t recommend reading your book while traveling. Some authors like to use this ploy to keep their readers’ attention, making them feel as if they are seeing it all firsthand. But I always recommend reading the book while you are in a new place. You’ll get the most out of it when you have to make a decision that you can’t make in your own home.
The good news is that there are plenty of examples of other people making the same choice, which is actually very exciting. The bad news is that there are plenty of other writers who just don’t know more about time travel than you do. You’ll have to read a few more of them if you’re ever going to make a book about time travel.
I have a feeling that we will probably see several more books about time travel before I die, so we need to figure out what to read first.