Visit: The Trevi Fountain (Piazza de Trevi, near the intersection of Via della Stamperia and Via delle Muratte). Allen's characters would be remiss if they didn't drop a coin in the Trevi, the ornate watering hole that was completed in 1762, though its origins date back to the Roman Empire. The fountain has been featured in "Roman Holiday" and "Three Coins in the Fountain," the latter of which pays tribute to the legend that a person who throws a coin in the fountain is destined to return to Rome.
View: Rome was built on seven hills, so there's plenty of spectacular views. One of the best is from the Cupola of St. Peter's Basilica in Vatican City. You can take an elevator to the top, but climbing the 320 steps is well worth it. (Be sure to dress properly, though: no shorts or miniskirts.) The Sistine Chapel, where Cruz's character cracks a lewd joke, is a short walk.
Shop in: Piazza Spagna (1 Piazza di Spagna and surrounding area). Allen may not be a fashion plate, but his upscale characters would certainly want to take advantage of the best Italian clothiers -- and it's here, at the Spanish Steps, that many of them have their flagship stores.
What if Europe isn't in your plans? Don't worry. There's always Manhattan, where the vast majority of Allen's 40-plus films have been made.
And if you want to really get off the map, take a trip to the Republic of San Marcos. Just remember: Change your underwear every half-hour, and please wear it on the outside so authorities can check.