I'm trying to track down my husband's favorite book as a teen/kid. It's about a Generation Ship with very utopian society. This colonial ship is traveling to try to reach 'heaven'; then there is a murder on board (the first), and there is an investigation into this murder. The cover of the book had a ship travelling through space, it looked like a wheel with spokes sort of. It would have been written before 1999
This is very probably Flight of Exiles, by Ben Bova. It's the second novel in his Exiles trilogy. The first two books are pretty hard young adult science fiction; the third book, End of Exile, gets a lot softer and more kid oriented. (However, I should note that Bova disdained the distinction between hard and soft SF.)
This is the original cover:
But there have been others, including this Italian one:
I'm not actually finding the cover I remember, which I think did have a spoked station on it. The space station/ship they are traveling on is definitely spoked.
Plot summary, per this review:
After a journey that lasted decades, the great spaceship the scientists exiled from Earth left on is about to reach the Alpha Centauri triple system. However, the long journey was tough for the on-board systems, which were not built for an interstellar expedition. To save resources, many people were placed in a cryogenic stasis but a fire causes the death of part of them.
Larry Belsen and Dan Christopher grew up like brothers but this latest incident becomes a reason of disagreement between them that can have important consequences on the continuation of the journey when they have to decide whether to try to colonize a planet in the system or continue the journey on a spaceship that is already at its limits. The origin of the division between the two of them is, however, in their common love for Valery.
In this situation, the disagreements between Larry and Dan broaden with each new decision about the future. Both of them are candidates to become the new Chairman of the Council, the body that governs the spaceship’s activities. When the planet that could be the future home for the crew starts revealing less than ideal characteristics, the two men start having opposite ideas about how to proceed.
Being the Chairman affects who gets priority in choosing a mate, which adds to the story's other conflicts. The strange collectivist government is probably what is being remembered as the "utopian" aspect. Moreover, I recall there is discussion about where they should consider stopping the spaceship, whether the world they might find will be a heaven or a hell. In the course of all this, one of the two men becomes the first murderer on board, and for a long time, the reader doesn't know which it is.