Yeah, I immediately thought of Druid City also.
Okay, the challenge is to find comics with contemporary settings (given a few decades of wiggle room) with no magic nor sci-fi elements. Action and adventure are prefered. Okay!
Bow, Cap, and Glasses by @Mr_Per50na s a modern gag-a-day comic in the Slice of Life genre. I find the humor hit or miss, but it's cute and the humor hits often enough that I keep coming back. Adventure themes are limited to getting lost while hiking in the woods and such everyman adventures.
You cannot get more realistic than a biographical webcomic, and Tiger in the Storm by @vfinnigan delivers a good amount of action. Here is some text copied from the series description: "Based on the journal of the late Maj. Gen. David Sawyer, Tiger on the Storm honors the 23rd Tactical Fighter Wing and their service in Operation: Desert Storm."
Oh yeah, Cars and Crimes by @JakiraJurosawa is set in the Roaring 1920s. That is far on the early side of your range, but it is within the 20th Century. It has car chases.
