As I've written before, we enjoy watching Rick Steves' television shows about travel, and make extensive use of his guidebooks when visiting unfamiliar places. Another resource that we found invaluable on our recent trip to Rome was a Great Courses series, The Guide to Essential Italy.
Neither, however, advises what we discovered for ourselves on our visit: Do as much as you can in the morning. For us, Rome was at its best before noon: the weather was pleasant, and the streets were delightful to walk through, with more locals than tourists in sight. Except for the most popular attractions, e.g. the Colosseum and the Vatican, crowds were low, and we were able to visit museums and churches relatively unjostled.
By noon, the crowds of tourists had begun to take over the city, and Rome under the afternoon sun suggested that we were back in Florida. The early evening mobs reminded me of taking Boston's Green Line buses during rush hour, and the threat of pickpockets became a much more serious issue.
As for eating, we found late afternoon to be a delightful time to relax in a restaurant after a hard day of walking and museum-browsing. Perhaps because Rome must cater to tourists, we found most restaurants open for a four- or five-o'clock dinner, with plenty of available tables and attentive staff. It was also still light, for better views, and relatively quiet—as it gets dark, the music gets louder, a correlation without obvious causation.
No doubt "night people" have an entirely different view of Rome, but this worked very well for us. Our only later-evening excursions were short walks down the street to the local gelato place, which soon became our nightly habit before falling into a deep and exhausted sleep.