NASA (National Aeronautics and Space Administration) has been running an Astronomy Picture of the Day since 1996. APOD is "originated, written, coordinated, and edited since 1995 by Robert Nemiroff and Jerry Bonnell."
Check About APOD for mirror sites in many other languages as well as APOD social media accounts (Facebook, Twitter, Tumblr, Reddit).
NOIRLab Image of the Week (National Science Foundation)
NoirLab tracks ground-based, nighttime optical and infrared astronomy, and posts weekly images of their observations and tools.