Our solar system is a bit boring on the big screen. It would take more than a month to reach even 10% the speed of light in a rocket. That's engines blasting for 35 days. And then engines blasting for another 35 days to stop you as you reach your destination. Then you're stuck since you simply cannot carry that much fuel.
Seriously, we can't even get to Mars.
But movies and TV shows rely on science that doesn't exist. Either stasis or
cryosleep would be necessary to get us anywhere with conventional propulsion.
Cryosleep Imagination
Sometimes cryosleep gone wrong can lead to time travel if the pods keep running for centuries. In this movie, Kirk and krew happen upon a centuries-old ship of supercriminals in stasis and they barely survive the confrontation.