If I was going to make a whole galaxy, I would start with a map. The star wars galaxy map would be a great inspiration. You'll obviously need to figure out how the inhabitants of your galaxy are dealing with the relativity problem (as in how are they travelling faster than the speed of light between planets?). Wormholes or "hyperdrive" is a common way around this idea. If it's wormholes, plot them on your map and make the colonies localized to that area.

After you've got your setting, I would work on systems of government. Is it a human dominated galaxy or are there many species involved. Do they answer to one central authority or do they govern themselves. Are there wars? What are the most valuable resources and why? How are the species involved competing for that resource. What are the socio economic problems? What are the "environmental" issues (maybe there's a black hole increasing in size affecting a major trade route, or maybe a star is on the verge of dying in one of the busiest systems).

From what we understand about technology at the moment, AI looks pretty much dead certain for our future. How do the people interact with "robots"? Are they classed as people? Are they slaves? Genetic modifications for the rich? What's the currency? What's the religions? It sounds detailed but it's stuff that would have a pretty big impact on the galaxy. If you can flesh all that out, the conflicts will create themselves, and where there's conflict, there's struggle and where there's struggle, there's a story.