My pick would have to be the A Whole Nother Story trilogy, in which (spoiler warning) you can only travel back in time. But because time is in a loop of sorts, if you go before the beginning of time, you will be at the end of time. From there you can go back to any time you want to. And time paradoxes cannot be produced. Plus, your memories from the previous timeline exist as well as the memories from the new one.
One of my favorite books. I try to visit locations mentioned in the book when i go to NYC. Re the Statue of Liberty arm - I had no idea about this history until reading about it in Time and Again. Actually, the arm was located in Madison Square park (not Central Park). When I visited Madison Square park, I looked for a plaque that might acknowledge this history but didnt find one. Anyway, great book!
Also, the arm and Madison Square Park are included in an episode of The Gilded Age (Season 1).
Loved Time and Again by Finney. It really felt like you were in those times.