Recently the ideas that sprang from the DeWitt in Titania have been coming back, not necessarily with the same focus or main character, but with the same ideas that were whirling through my head. I'm realizing what was running through my head wasn't necessarily clear in that little tidbit, but there's a lot of stuff. And surprisingly, a lot of it are necessary answer to questions. Here are somethings that you should think of in your sci-fi setting. And yes, totally feel free to add in the comments.
Even if not set in this universe, you have to figure out how far in the "future" the technology is. Have we mastered space colonization? Long distance travelling? What is the next evolution for the internet? Cell phones? Entertainment? If it's recent, you may want to look at what people predict for the next ten, twenty or fifty years. When you go significantly past that, it's easier to be a bit more creative. I would still suggest research what tech people are researching now, but expanding on that sometimes is great inspiration.
WHAT HAPPENED TO THE HOMEWORLD.
With a lot universes, this means Earth, but for any story setting every people has a place of origin. Is it still where they stay? Does it still exist? Do they even remember it? That last one was a great premise I first saw from Asimov. But it's important to know what happened to the biological home. If you're not traversing space in the story, it's important to know how the world started and how the tech has changed the world, for the better or worse.
Even if you're staying on one planet, even if there are no extra-terrestrial beings, you have to decide what the origins and values are of the race you're writing about. And if there's more than one, what's the relationship? Sometimes looking at the historical relationship of neighboring countries is great inspiration. Also looking at different cultures throughout the world, maybe even further back in the past when globalization was less present, and people were more isolated.
WHY IS IT A SCIFI?
If it's a story that doesn't need to be set in the future, do not write it in the future. The same can be said for adding extra tech or extra species. The setting has to enhance the story, and if it doesn't just keep it in modern times or historical fiction. Sci-fi doesn't make things extra exciting by merely being in space or in the future. It takes elements of the story that already exist and reveals them in a new light.