It's a fine thing to go back once in awhile and read the old award winners. Free SF Online collects these, and recently put up The Big Time, a 1958 Hugo award winner from Fritz Leiber, by way of Project Gutenberg. Leiber is well known for his fantasy, but he had fine hard SF chops too.
A good time travel story almost always acknowledges that the very possibility ties things in complete knots. This story does so quite well, telling of a Change War taking place across all human history, and humanity is only one small part of it. The setting is a R&R station, the protagonist an "Entertainer", kind of like a geisha or call girl or something, but there are male versions too. The Places are outside the regular time stream, on a meta stream called Big Time. They end up with a tight internal drama to solve.
The story reads a little weird, and for me was hard to really get into for awhile, but it builds very well. Each episode brings out new things in the characters, and in the end what looks like a very hopeless long term term situation is explained with great finesse to be in the natural order of things. It's a really satisfying story to read, in the end, and not at all surprising that it won the Hugo. I give it four stars, you should go right out and read it.