Star Wars. You get all this military action between the government and some insurrectionists (and some exposition about embargoes and galactic politics) but you don't ever get a sense of what life is like in the galaxy for the average citizen. Is the Rebel Alliance quietly supported by most people? Is life under the Empire repressive? How did things change after Palpatine took over as Emperor? Can everyone in the galaxy even be bothered to give a shit? I'd be surprised if there isn't an EU book on this. Marvel has a couple things like you want that I can think of. Marvels is a beautiful miniseries about a newspaper photographer at different points in the early Marvel U. And Damage Control is about the company that cleans up after the heroes and villains just about destroy everything. I haven't read that one but I'm aware of its premise.
I think the closest we've gotten to that sort of story so far is the first season of Rebels. While it is about a group of people fighting against the Empire, the entire season is basically contained to the planet Lothal. As the main characters hit the Imperials where and how they can, you get small glimpses of how the regime is affecting the little guy - a disgruntled shopkeeper cowering at the barrels of stormtroopers' blasters, a farmer and his family taken prisoner when the refused to give up their farm, a kid joining the Imperial Academy because his sister did the same and was never seen again. That was really one of the strengths of the season for me, so I'm not really sure how I feel about the series expanding toward the scale of the Galactic Civil War next season.
This to me was one of the main draws of Star Wars Galaxy the MMORPG released by Sony Online Entertainment in 2003. It eventually suffered a painful, protracted demise, but up until that point it was a very fun look at the Star Wars universe; it let you customise your characters skills to a pretty significant degree, choosing from combat skills, healing, crafting and even entertainment and politics. If you wanted to live the life of a small town moisture farmer on Tatooine you totally could, hell you even had the opportunity to corner the market on such things because of the player driven economy. I remember trekking across Naboo by landspeeder to visit a tailors because I wanted to dress my NPC vendors in fancier clothing and I had heard, through word of mouth, of this fantastic little village hidden away which had deep discounts. I am not sure any other game has since captured that minutia of the Star Wars universe (or any other fictional one for that matter), while still allowing players to choose their own story and give their characters the life they want them to have.
In the (Disney-denounced, but screw Disney! There will only ever be 6 star wars films!) EU, there are a lot of books that give other perspectives. Probably the "Tales of/from X" series is best for that, simply because it's a collection of short stories rather than a single large scale tale.