Haven't been to Venice or Abruzzi, so this is for Rome only.
Don't eat lunch or dinner within 3 blocks of the Colosseum in any direction, even if Rick Steves says it's OK. Had my 2nd worst meal ever in Europe at a place he specifically recommended.
It's gonna be really hot in Rome in July, like 100F hot. Go to Goodwill and buy some light silk/rayon short sleeve shirts that look European for $5. They'll probably be "dry clean only" but you're only gonna wear them one or twice so you don't really care.
If you go to the Catacombs/Via Appia, do yourself a favor and drive a little farther south to
Ristorante L'Archeologia. It's unique and well worth the visit, IMHO.
@8893 is right - while everything I had here was amazing, it's where I was introduced to lardo on lightly toasted bread with a sprinkle of lemon. So simple yet so wondrous.
You can get museumed out. I did, after visiting the Vatican and a couple other places. It was in the middle of the Borghese, where I'd just had it up to my eyeballs with religious imagery. Unless you're truly a student of classical art, prioritize which ones are really important to you and leave plenty of time for sipping wine while watching the scenes at the various piazzas, particularly Piazza Navona. You might run into a street performer who absolutely nails the closing solo of Comfortably Numb. Anyway, plenty of delightful unscheduled street performance abound.
Save one night for a dinner in Trastevere. Doesn't much matter where. Great outdoor dining scene everywhere.
If going to the Trevi Fountain, there's a really neat gelato shop couple of blocks away. Il Gelato di San Crispino. Looks like a science lab, but it's the best we had. The snozzberry tastes like snozzberry.
Visit a market. Usually guidebooks will list Campo d'Fiore as #1, but it's become too touristy. But any market will do for grabbing a few things to eat on premises or bring back to your hotel. If you've never eaten a fresh artichoke, you'll find folks to prepare one for you which you'll eat like a lollipop. You can't get that in US.
Don't order a cappuccino after 11am.
I'll probably think of others, but that's it for now.