Your schedule looks good. Only advice I'd add to the already fine ones listed here is to be flexible if you see the weather not cooperating. The Forum,etc. is much nicer to see when it's not raining.Mid-September may bring some showers,especially in the afternoon.

Agree that your Day 1 is a little light- the Pantheon won't take too long (we did the audio tour and it was maybe 20-30 minutes?)

I think we were in Vatican City half a day (toured the museums with a guide, then did the Sistene Chapel on our own; wish we had done the tour that included both as the information was very good).

We had a very good lunch at Cavour 313 which is sort of near the Colosseum, etc.

We also did a guided tour with Angel Tours that included the Colosseum, Forum, and Palatine Hill. Definitely worth it as we don't know a ton about ancient Rome and the tour group was limited to 6 people so my husband got to ask lots of questions. It meets at 9 am so you will have the afternoon free.

http://www.angeltoursrome.com

The park around the Borghese is lovely, but the museum itself was my least favorite stop. Is that terrible to say? Oh well.

Finally, we had two great meals at Cul de Sac near the Piazza Navona.

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