The Amalfi coast is simply breathtaking - you have to see it once in your life, preferably with a loved one, and ideally on your honeymoon (if it's not too late, or too early, for that). Craggy mountains, whose lower slopes are painstakingly terraced with lemon groves or dotted with gravity-defying villages, fall sheer into seas which are fringed with needle-like rockstacks and implausibly clear waters; beyond, the chi-chi island of Capri shimmers on the horizon. Granted, it's expensive and crowded, especially in midsummer, and can feel a little desolate out of season, but if you get it on a clear, warm spring or autumn day (and there are plenty of these), its dizzying seascapes, picturesque towns and ubiquitous scent of lemons will remain with you for years to come.
Naples is the perfect counterbalance - vibrant, colourful, packed with world-class art and architecture - and a worthwhile city break in its own right. It's also a good base for exploring the uniquely preserved Roman cities of Pompeii and Herculaneum, and scaling the (still active) volcano which destroyed them, Vesuvius.