The basic plotline is two couples in a time machine travelling through a series of universes, more or less similar to our own, alternately running from and chasing the villains that tried to kill them at the start of the story.
But what it really is, is a homage to 1930s pulp science fiction. The style is dated and the characters are Heinlein usual combination of intellectual brilliance, excessive heteronormative sexuality and stereotypical gender norms. Interestingly, Heinlein spends some time exploring the unconscious ways in which men undermine women's assertion of equal rights and self-determination while believing that they are being supportive. It is surprisingly insightful, given Heinlein's justified reputation for reactionary thinking.
The book is full of in-jokes, most of which I didn't get, not being steeped in the fiction which the book is paying homage to. I liked the concept of fictons - that somewhere in the multiverse any fictional world thought of pops into existence. That would be cool. Of course, Lilliput, Barsoom, Oz and Wonderland wouldn't be the worlds I'd choose to visit but there you go.
I hated the ending where Heinlein brings all his characters together for a big, self-congratulatory conference. This is strictly one for the fans.
So, if you could visit any fictional world/universe where would you choose to go? I'd go to Sunnydale, Westeros and the Culture.