I've seen "Cavalleria" many times. It is my favorite opera. It's short (~80 minutes), and is always shown in a double bill with "Pagliacci," so you inevitably get two operas for your money. Although the theme of "Cavalleria" is ugly, it has a higher concentration of beautiful music than any other opera I've seen or heard. You've already commented on the famous "Intermezzo." There's plenty more great music, starting with the overture and the first aria, as well as "No, No Turridu." But my favorite is the Easter Mass, which is a grand and masterful combination of chorus, orchestra, processional and soprano singing. Truly a great experience.
If you can't get to see it live, buy the DVD of Franco Zeffirelli's 1982 production starring Placido Domingo, Elena Obratzsova and Renato Bruson. It was filmed on location in Sicily, not on a stage, and is just fantastic. DTS sound, too.