Much like their New York namesake, this Albany-based band hasn’t taken much of a rest. Originally from the Hudson Valley area, these five guys—ironically, with all four-letter names— have already shared the stage with the likes of Paramore, Saosin, Owen, Acceptance and Halifax. Guerilla Magazine called The City Never Sleeps a “refreshingly hard-to-categorize rock outfit…unsigned, relatively new on the music scene, but undeniably catchy.”

Curt Mulick became a drummer after a telltale twist of...