I think the early seasons of CSI really captured that early 2000s vibe. Someone mentioned Monk. I faithfully watched that show, but it lasted from 2002 till 2009 (which is more mid 2000s) and it just has more of a timeless feel to me. Maybe because it didn't really try to be that hip. I was much too old for Lizzie Mcguire, but that show seems to capture early 20OOs teen culture.