Mix of both light and deeper shows here, mostly character-driven:

Scrubs - Show about a group of residents at a hospital navigating their first few years of training.

Cougar Town - Show about 40somethings in western Florida, the name has nothing to do with the show after the first five or ten episodes. Same creator as Scrubs. Focuses on the core group navigating life at 40 in Florida and their ridiculousness.

Community - Show about a community college in Colorado that gets increasingly experimental in its story telling. Show focuses on the antics of the core group.

Better Off Ted - Another show about 40somethings, this time in the corporate world. The name, like Cougar Town, has almost nothing to do with the actual show. Focuses on how this group tries to keep ahead of their soul crushing jobs for a corporation that's literally evil.

Happy Endings - This time about 30somethings in Chicago who are all friends, two of whom are about to get married when the bride runs away at the altar. Really turns into putting this group into various scenarios to see how it plays out.

New Girl - Show about a teacher in LA who moves into a loft with three guys (sometimes a fourth) and their subsequent misadventures in the city.

30 Rock - Show about the cast and crew of an SNL-style variety show airing weekly on NBC out of 30 Rockefeller Plaza in New York, grows increasingly absurdist over times.

Arrested Development - About the son of a real estate tycoon who gets arrested for so many crimes and how he tries to keep the family business going despite the incompetence of the rest of the family (and occasionally his own incompetence).

Bored to Death - About a writer who solves mysteries with his publisher and best friend (two different people).

Only Murders in the Building - Show about three residents, two older and one younger, of a classic New York residential building that discover they like the same murder mystery podcasts and then start their own true crime podcasts when they discover a murder occurred in their building.

Veep - About a put-upon Vice President of the United States and the general incompetence of her office and the administration. Surprisingly insightful satire of the actual executive branch in the United States.

Silicon Valley - Show about a group of guys in Silicon Valley and their VC partners trying to build a startup.

Happy to recommend more if you've got something more specific you're into.