One side-effect may be that emo music isn't as popular, since young Americans wouldn't need it to proverbially drown their 9/11 sorrows. Pop-punk would probably remain more in the louder, '90s Green Day/Offspring mold for another few years rather than transition to the style of Dashboard Confessional and other emo bands. Jimmy Eat World was already on the rise, though, so this may just be delaying the inevitable. Maybe the two would coexist into the Noughties?
And speaking of Green Day, they probably wouldn't have had the career resurrection that they saw after American Idiot. They may record an album with similar themes, but it won't strike the same chord that they did in OTL -- the young, disgruntled, anti-war listener base that turned it into one of the biggest albums of the decade won't be here this time. They'll likely break up, slide into the mists and remain associated with the mid-late '90s, like Blink-182 did, rather than becoming international megastars.
The culture wars would definitely have been more heated. You wouldn't have 9/11 to help unify socially liberal New Yorkers with religiously conservative Texans as proud, flag-waving Americans, so instead you've got both groups still calling each other godless queer-loving secularists/Bible-thumping bigots. I think you may very well still see a Jesusland map ITTL, albeit a slightly different one. Cultural/moral issues will loom much larger in the 2004 election, rather than national security.
The Fox News Channel is less of a juggernaut, since it can't cash in on 9/11 and War on Terror hysteria. The Daily Show probably would've still continued its track towards more serious reporting, as the seeds for that had been planted with Indecision 2000.