The historical area in the city center is much bigger than people think, it could take 3/4 days just walking around to see everything, without stopping for a visit, so take that into account.
Also, it's pretty hot right now (around 35-37 degrees Celsius), mind that too.
I won't give you the usual list of monuments and such, you can find all about them in any travel guide or IG/tik tok account, but don't miss the visit to Colosseum and the forum (especially the forum),book tickets in advance it'll save you a lot of time at the ticket office under the sun, do the same if you thought about visiting the Vatican museums.
A spot that's not usually under the radars is Terrazza Caffarelli (https://www.terrazzacaffarelli.it/) on top of Campidoglio (Capitoline Hill), you'll find a nice rooftop bar there with a beautiful view.
Edit: I totally forgot about the Museum and Crypt of Capuchins in Via Veneto, there's a San Francesco painting by Caravaggio and, if you are not disturbed by that stuff, a crypt entirely decorated with monks' bones and skulls. There are literally hundreds of them and thousands bones. It's pretty unusual, but kinda great if you ask me.
I'm biased because I live there, but if you wanna eat near the Colosseum my advice is to try Taverna Romana for roman recipes and Tettarello for pizza. Those are two of my favorite places to eat in Rome in general.
I don't know how long are you staying but if you get the chance go to the beach one day. The south is the best, especially Sabaudia that is just below Odyssey's famous Mount Circeo, but you gonna need a car to go there.
https://www.viaggiando-italia.it/wp-content/uploads/2022/03/...
Anyway, enjoy the visit!