One week in Italy

This is is good site to read to get ideas on logical places to go to from wherever you are entering the country
https://wikitravel.org/en/Italy

Here are Rick's ideas about Italy. First click Plan and see his suggestions for one week; then click At A Glance and read his capsule impressions of various places. https://www.ricksteves.com/europe/italy

If you want more specific suggestions, you'll have to give us more information. What do you want out of your Italy trip? Why are you going there instead of another place? How do you do in heat? Are you going alone or with others? How old are you? Are there any places in Italy you think you want to visit or avoid? What kind of places have you liked or not liked in prior travels? Have you even had prior travels, or are you new at traveling? Do you like car museums, Renaissance art, strip clubs, mountain climbing, designer clothes shopping? Help us help you!

Rome is amazing. You might be able to see Florence as well.

If you do both, Rome for 4 nights and Florence for 3.

For a first trip to Italy, I would recommend Rome and Venice.
Those are my favorites.
I've not yet been to Florence, but I'll be there later this year.

Rome, Venice and Florence are all wonderful, but will be packed with tourists. Depending on the type of traveler you are, I would head to a few places that will still be crowded, given the time of year, but perhaps less visited than the three main places first time tourists go. With that said, if you're arriving in southern Italy, you might consider Basilicata - Matera is stunning. Stay in the Sassi - (otherwise known as caves). They're beautiful, cool in hot weather, and something you'll always remember. If you like history, read "Christ Stopped at Elboli," by Carlo Levi, then visit Aliano - up in the mountains, where he was exiled during Mussolini's reign. It's a small, but beautiful town, with historical significance. While I haven't yet been there, Maratea - a beach town in Basilicata - not to be confused with Matera, is supposed to be beautiful. A friend, who lives in Basilicata, has coined it her favorite beach, and it won't be overrun with tourists like the Amalfi Coast. I have two friends who are tour guides in Basilicata; one who resides in Matera. Feel free to send a text if you'd like contact information.

I would avoid Venice. We were there the last week of April, and it was crazy crowded! They actually had to put up barriers to control the crowds! The sheer numbers of cruise ship passengers have impacted this beautiful city in a negative way. The Cinque Terre is also hard to enjoy with so many cruise ship tourists. Rome is amazing, but it will be hot. Our absolute favorite place in Italy is Lake Como----particularly Varenna. We also loved the Amalfi Coast, but stay in Salerno not Sorrento and utilize the ferries to explore the coast. You can also get to Pompeii from Salerno. You will LOVE Italy!!

I think in August I'd avoid both Venice and Florence because of the crowds. Rome's huge, so even with lots of crowds, you can find places that are enjoyable - though maybe not the top sights like the Colosseum. Churches are open from early morning - even St. Peter's isn't likely to be crowded at 7-8 am. Also consider Bologna, which is not a big tourists destination. It's a rail hub, so it's a very good choice for day tripping to other not-so-crowded towns like Modena, Ferrara and Padua. You can also day-trip to Florence and suffer the crowds to see the highlights.

I would do Venice and Rome, except for the fact that you are talking about August. Where are you going after Italy?