Recommendations for off the beaten path underground/ancient sites in Rome

You sound like my kind of travel companions! Have you visited the Basilica San Clemente? I am unsure how crowded it will be, but it will certainly provide a welcome relief from the July heat to be 2-3 levels underground in the excavation areas.

One of our favorite underground sites is Domus Romana at Palazzo Valentini near Trajan's Column.
The archaeological remains of ancient Roman houses uncovered beneath Palazzo Valentini are now on permanent display.

https://www.palazzovalentini.it/

We visited the catacombs of Priscilla. That is the only catacombs we have been to and, because it is in a less-visited area, we ended up having a private tour after we waited about 20 minutes to see if some other English speakers showed up and none did.

Near the Pantheon is Hadrian's Temple. Still having the original columns from one side of the buidling from year 145. It's cool to look at from the outside. But its free to go inside. There is a 20 min video inside that goes into pretty good detail about the history of Rome. It explains what Hadrian's Temple is, and then what it was used for throughout history. If you look on one of the columns you can see a cross that was made 1500 years ago when it was a hospital. It was really worth it, free, AC, and quiet. Only 3 other people were watching the video with us. I highly recommend it.

Thank you to everyone for taking the time to respond These are all perfect. I am looking forward to exploring everything mentioned.

Two more ideas. One is literally underground, although not what you meant:.

Read all of the funerary inscriptions and their translations in the underground passageway between the two buildings of the Capitoline museum —- especially the ones for children. You will really get a feel for how the ancient Romans thought about family, fame, life, and death.

Try to see the swarming flocks of starlings in the evening through the open ceilings of the Baths of Diocletian.

See other posts here, like this one: https://community.ricksteves.com/travel-forum/italy/unusual-ideas-for-rome

We do have a special interest in exploring “underground”.

On week-ends you could visit the Domus Aurea, Nero's Royal Palace that's underground near the Colosseum.

Another plug for the basilica San Clemente. Right near the colosseum. It’s a church built on a church built on a Mithraic temple.

There are also a couple of catacombs out of the Appia Antica.... which is a great "Ancient Rome" walk on its own, either for just a couple of miles or a few more than that.

St. Callixtus:
https://www.catacombesancallisto.it/en/index.php

San Sebastiano:
http://www.catacombe.org/uk_index.html

Parco Appia Antica:
https://www.parcoappiaantica.it

San Nicola in Carcere has some ancient Rome both underneath the church and visible from street level; there are exposed columns of 3 temples dating as far back from third century BC. incorporated into the exterior. The temples' bases are below ground, and can be visited during posted hours.

https://www.turismoroma.it/en/places/basilica-di-san-nicola-carcere
https://en.wikipedia.org/wiki/San_Nicola_in_Carcere

San Clemente is very interesting as it covers a number of different eras the further down you go.
However, don't bank on it being cool underground.
The Vatican Necropolis is humid, hot and stifling.
We didn't know this and brought warmer clothes that day to go there one June day.....big mistake!
Bring a hand fan, water, a cooling neck towel and a little spritz bottle of water to spray your face and neck.
Whew...we couldn't wait to get above ground again!
I don't know about San Clemente, as I was there on a cold weather day, and it's a lot more open lower down...not so closed in.

Thank to everyone for the additional ideas. They are all perfect. I have created a list to use (since open days and times change I did not include them here.) Should be a quick copy and paste for others that are interested. We travel in July so I will update if needed.

Basilica San Clemente
https://www.basilicasanclemente.com/eng/

Domus Romana at Palazzo Valentin
https://www.palazzovalentini.it/

Catacombs of Priscilla
https://www.catacombepriscilla.com

Hadrian's Temple
Note: Go inside and watch the video

Read all of the funerary inscriptions and their translations in the underground passageway between the two buildings of the Capitoline museum. https://www.museicapitolini.org

Domus Aurea, Nero's Royal Palace
https://www.coopculture.it/en/poi/domus-aurea/#55

St. Callixtus:
https://www.catacombesancallisto.it/en/index.php

San Sebastiano:
http://www.catacombe.org/uk_index.html

Parco Appia Antica:
https://www.parcoappiaantica.it

San Nicola in Carcere has some ancient Rome both underneath the church and visible from street level; there are exposed columns of 3 temples dating as far back from third century BC. incorporated into the exterior. The temples' bases are below ground, and can be visited during posted hours.
https://www.turismoroma.it/en/places/basilica-di-san-nicola-carcere
https://en.wikipedia.org/wiki/San_Nicola_in_Carcere

This might be useful to review and download in advance if you do some of the Appia Antica. It sort of hard to find if unfamiliar with the website, thus the link.

https://www.parcoappiaantica.it/wp-content/uploads/2021/11/via-Appia-Antica_ENG.pdf

More good stuff here:
https://shop.parcoappiaantica.it/visitare-il-parco/audioguide/

https://www.parcoappiaantica.it/faq-2/

While it is not underground, have her check out Ostia Antica and see if it holds any interest for her. Easy to get there using public transit, and not usually crowded at all.

You seem like two people who would also like the National Etruscan Museum in the Villa Giulia --- it's one of my favorite museums in Rome.

Another vote for San Sebastiano! We enjoyed Catacombs of Priscilla but found San Sebastiano to be next level. The relics of Saints Peter and Paul were stored there. There are intimate chapels, very well preserved Roman tombs, in addition to the expected loculi. Casa Romane Del Celio beneath San Giovanni and Paolo is a collection of about twenty rooms from an apartment building and Roman houses. For me, a huge history buff, the Mamertine Prison was a big deal. You can go down into the holding cell to where the prisoners (many of high value) were held waiting for execution. They were dropped through a hole in the floor, which is still there.

You might enjoy some of the lectures from this free online Roman Architecture course offered by Yale.

https://oyc.yale.edu/history-of-art/hsar-252

hey hey grand grand tour
another “off the beaten path” that may interest you
wantedinrome.com
lake nemi: pristine waters and an ancient mystery.
Italymagazine.com
lake nemi and it’s wild berries
short train ride from Rome to countryside, where the pope has his summer palace/garden
frascati village
known for white wine, take a wine tour, visit ceralli.it. small bakery/pizza oven making the “best porchetta”,
lake nemi and it’s history of goddess Diana, known for wild strawberry planted upwards of the hills. using the berries to making anything and everything.
withlocals.com
check rome area. there is a “beautiful countryside day trip: castelli Romani
pierpaolo does tour, you can email/contact him for a longer tour. born in this area, away from the hustle/bustle and see the countryside.
aloha

Basilica San Clemente! We were just there in May and you have to explore all 3 levels!

This nighttime event might be of interest https://www.viaggioneifori.it/en/. One of the best after dark things we ever did there.

Maybe take a look at the book Secret Rome by Jonglez. Available via Amazon.

https://www.booktopia.com.au/secret-rome-6-e-jonglez/book/9782361952006.html

I’m also interested in underground ancient sites. In 2018 I took a really interesting tour with Walks of Italy. Here’s the link for the current version of that tour which is called Crypts, Bones, and Catacombs: An Underground Tour of Rome.
https://www.walksofitaly.com/rome-tours/rome-catacombs-tour/

In addition to the Capuchin Crypt, we visited a number of church catacombs (Priscilla and San Clemente among them).

Have fun planning your trip.

The tomb of the famous patrician Scipio family at the beginning of the Via Appia. Access with guided tour only, details:
https://sovraintendenzaroma.it/i_luoghi/roma_antica/monumenti/sepolcro_degli_scipioni