We went to Rome in October and had the best time. Would warn Rome in August will be very hot and humid and super busy.
Some food/drink recommendations from my husband's friend who grew up in Rome and still spends a lot of time there -
https://www.trapizzino.it/en/ for delicious streetfood like pizza but in a pocket shape - we visited the one in Trastavere but there are a few outlets across the city
Santa Trastavere was a cute spot for dinner/drinks
404 Name Not Found is a cute bar
Slow Wine Beer Food was so good for pasta - but was cash only
Visit the Patheon first thing in the morning on a weekday - its free and you hopefully wont have to queue much.
Book the Colosseum online before you go don't get sucked in by ticket touts.
We didn't do the Vatican this time as I've done it before but again I think that's one to book online ahead otherwise you'll be queueing for a long time.