Four nights in Rome before joining a tour

You do not need advanced tickets for Ostia Antica. You can get to and from Ostia easily on public transportation. Take the train from Roma Porta S. Paolo.

For us, walking a couple hundred yards on the Appian Way was enough to get the idea. To save some time in your packed schedule, you could pick up the bus back to the baths. But, it might be a good idea to build in a little extra time for waiting for the bus. It only runs a couple times an hour and on a Sunday (maybe that makes a difference) we had to let a couple go by because they were so crowded we couldn’t get on. Depending on your walking speed, it might not pay, but for us it was worth it the wait.

Also, consider visiting https://travelsetu.com/guide/capitoline-hill-and-museums-tourism
and Trajan's forum.

A couple of beautiful churches you might want to see while exploring Trastevere: Santa Maria in Trastevere and Santa Cecilia in Trastevere. If you get to Santa Cecilia, be sure to see the colorful crypt. I think it closes earlier than the church itself.

Two much smaller churches closer to where you're staying have beautiful mosaics--Santa Prassede (the prettiest) and Santa Pudenziana (the oldest). Small churches like those often have extremely limited hours. Some have a very long mid-day closing period; others aren't open in the afternoon at all. This is my years-old information for those two, supplied just to give you an idea of what you might run into:

Santa Prassede: 10 AM to noon and 4 to 6 PM
Santa Pudenziana: 9 to 11:30 AM

Especially in small churches with no entry fee (like the last two I mentioned), you'll want to have some coins to feed the light boxes to better illuminate mosaics and/or frescoes. I imagine 1-euro coins will always work, though it's possible you might need two of them (inflation!).

We went to Santa Prassede and Santa Pudenziana on acraven's recommendation. They didn't disappoint. One of them was slightly hard for us to find, our navigation had us on the street behind the church, so you might need to look around a bit. They were amazing. They did get large tour groups, and absolutely bring coins.

Thanks for the tips!!!

Easy train ride to Ostia.

Thanks - the plan is firming up with no major changes - just some tweaks.

For the morning of our last day, I plan to offer up 3 options to the other 3 folks in my group. We'll have about 2.5 hours. We can all go together or split up in groups of two.

Option 1: Capitoline Museum
Option 2: Churches (St. Peter in Chains - San Clemente - Santa Pressede)
Option 3: Shopping (open to suggestions for best places not too far from our Monti apartment which is near St. Peter in Chains)

A couple of thoughts. I would use the train for Ostia Antica. The train stop is right at the entrance to the park. There have been reports here that getting a return taxi from the park is difficult. The park is a little isolated so the only taxis in the area will be taxis dropping off other people. The train is very easy. Second, we always stay in the Termini area just for the convenience to transit. However, Monti is a decent location. We always work a nap in on the first day but with a 2.30 arrival you are running out of time that day. The taxi from the airport is fixed for four people so that will be cheaper than the train. Remember, you can only get taxis at designated taxi stops. You cannot hail a cab on the street as you would in New York or Chicago. And, if you call a taxi, the meter starts when they get the call so it will arrive with a couple of euro on the meter. It is not a scam. And -- if paying via ccard, make sure the card reader is working BEFORE you get in. It is a busy schedule but you should be OK.