So to be cliche, when in Rome, do as they do – namely, get out and walk! Don’t bother with a cab unless you have to get to the opposite end of town quickly, you’ll be doing yourself a disservice. And for the love of God, invest in good shoes before you go. A trip to a specialty show store (REI comes to mind) is a Very Good Thing.
Once you get there, look at a guidebook of what you’re into seeing, and get going. Be leisurely! There is great stuff around every corner.
Stop and enjoy yourself; this is from the table as we were having an espresso at around 10am. And don’t mind if the weather is lousy (it was raining off and on this day for us); that cuts down on wimpy tourist sorts. And photographers are about the polar opposite of wimpy … usually we’re more adventurous, if not downright tresspass-y and obnoxious. After all, I got scolded for trying to lay down near the center of the Pantheon to get a wide shot of the ceiling. No clue what the guard said, but it may have been very animated Italian for “damn photographer!”
A word of warning though: protect your valuables, including gear. Do NOT carry your passport around. And keep your wallet in a front pocket … mine was in the smartphone pocket of my jacket, just under the cross-strap I use for my camera. Non-obvious camera bags are also good – my wife had one disguised to look like a handmade leather purse. And if you can, travel with another photographer (buddy system, just like school field trips!) and switch off who shoots and who keeps an eye out for trouble.
Above all, thought, have fun! And if you end up exhausted, a cab back to your hotel (or somewhere for a drink – I recommend Scholar’s Lounge off Piazza Venetzia, best Irish Pub in Rome) is not a sinful thing. Not by a long shot.