The Speed of Light Is a Relationship Between Time and Distance

Without a warp drive, you pretty much can't have any space stories because it would just take too long to get between planets or between parts of the galaxy. It really effectively limits you to operating in a single solar system. But if you're patient, you could send out the exploration teams which could discover those other star systems. So you could realistically still have first contact stories, but you can't zip back and forth between stars that are really far apart.