If going to the airport, I've been told to plan around an extra 30 minutes for the airport test. I also heard that there is a test center in the Termini station. I've also noticed there is a hospital south east of the Colloseum that is testing - Ospedale San Giovanni Addolorata.
One thing to consider, and what my Plan A is: Check out https://www.ellumehealth.com/ for your particular situation (Delta is partnering with them, I don't know what other airlines are doing but suspect it will be universally accepted by US airlines since it qualifies under the US entrance requirments).
You must purchase the test and setup the app before you leave for your trip. Up to 72 hours before you return home, you take the test from your hotel with a prescheduled video proctor and get certified test results within 15 minutes via your smart phone.
Delta has links directly via their website to purchase for $50+S&H however CVS currently has them on sale for about $30 which includes S&H and then you just purchase the proctor independently for $15. My understanding is that multiple people can do a test together via one proctor session so you can save some money and time going this route.
HTH