[omnibrain]

If you want to visit St. Peter in the vatican, it's free, but there can be significant waiting time for entry. But you can rent an audio guide (online in advance) and skip the line.

Similarly, if you want to visit any museums, especially the vatican museums, book in advance and skip the lines.

Ostia Antica is worth a visit. It's the lost and "sunken" harbour city of ancient rome. You can roam there freely and explore a ruined city and discover 2000 year old mosaics and wall art.

Romans (and italians in general) like to eat late in the evening. So if you want to go out for dinner, but have no reservation, you can try to arrive early (6pm) at the restaurants or pizzerias and tell them, that you are just interested in some quick dinner and will be gone before their "regular" patrons arrive. That usually works.

If you need to drive a car in Rome: Don't. If you must, avoid the oldest parts of the city with the narrow streets.

[bombcar]

For the Vatican I found that getting there very early (as early as they open) his recommended. Lots of things open before they get really busy.

Also if you want to skip the Vatican but still see old churches, well Rome has a few.

I highly recommend dedicating at least some mornings to just walking around, everything is in relatively close proximity in the central area.