Early morning runs in Rome

I would wait until the sun rises after 7am around that time of year.

I would think so. We are early raisers and I seen a few joggers at that time.

I would think so too. We're also very early risers and enjoy being out on (largely empty) streets before most tourists are out of bed. Early mornings would be a good time to run without having to dodge lots of people, and I wouldn't worry about personal safety.

Sunrise charts list May 1-7 times around 6:00, give or take.

https://www.timeanddate.com/sun/italy/rome?month=5&year=2017

Although we only walked, the paths along either side of the Tiber River are magic. I'm not talking about the ones down near the water, but the ones up along the street. By 7AM or so there will be plenty of traffic so be careful crossing (because they don't STOP!) but it's a run you won't ever forget.

Yes, safe at any hour. Like anywhere, keep your wits about you. Violent crime is rare and pickpockets like to work crowds. You'll see normal Romans with early jobs out-and-about.

Villa Borghese would be another good spot for a trot. The park is really big so there's plenty of ground to cover.
I'll second Jay's vote for running alongside the Tiber as well.

It will be light before 7am. It's light already now at that time. I ran the Rome marathon today and can tell you I run every time I'm here which is several times a year. Via Del Corso is nice and deserted early in am . I frequently run down to the Colosseum and it wonderful early in morning. Also along the river you will find other runners. Enjoy your runs!

Wow so many helpful comments so quickly. Thank you all.

I'd feel totally safe doing it. These areas are all pretty central and do have decent police presence.

You ain't kidding, stapled...

One early morning we left our apartment at Campo de' Fiori and walked down towards the Tiber for a stroll. Almost there, we literally ran into two soldiers carrying Kalashnikovs. I figured it was either a government building of some kind or an embassy. In our Rome travels, we counted no less than 15 embassies in various parts of the city, all soldiered up with machine guns to the hilt.

Also heavy police presence at Spanish Steps and Trevi Fountain.

Here is a website with live webcams around Rome, and other places, that you can use to check on what it is like at different times of the day or night.

https://www.skylinewebcams.com/en/webcam/italia/lazio/roma/scalinata-piazza-di-spagna-barcaccia.html