Yes, parades are full of beads, booze, and debauchery, but there's a whole lot of culture and history in there, too. Originally founded as a social aid organization in 1916, the Krewe of Zulu quickly became known for its spoofs of Carnival royalty. During the 1960s it became the first African-American parade to march down St. Charles Avenue and Canal Street, traditionally reserved exclusively for white parades. If you're into learning more about their history, check out the Zulu Lundi Gras Festival on Monday before heading to their parade bright and early Tuesday morning to try to catch one of their famous coconuts.
A less publicized but equally elaborate celebration is that of the Mardi Gras Indians. Their parade dates, times, and routes, are never published in advanced and are generally pretty lose, with groups splitting up into two tribes and engaging in symbolic fights whenever they meet. Check with locals once you're on NOLA ground to see if you can get the inside scoop, but the parades always take place on Fat Tuesday and can be usually spotted in Treme and Central City.