Activities in Rome without a reservation

Certainly of course are the fountains, and the main piazzas (Campo di Fiore, Navona Spanish Steps) The pantheon, I believe a time can be reserved on short notice, while the Trevi Fountain has a fee and Queue, you can still walk by and see it, the queue is just to get to the lowest level in front of the fountain.

Castel San Angelo always used to be walk right up and get in.

I can also add that almost any church is "walk right in" and there are lots of hidden gems. If you happen to be walking and see something indicating a church (they can be pretty non-descript from the outside) step in and have a look, it is amazing what might be tucked away.

Sistine Chapel

The Sistine Chapel is definitely not a spur-of-the-moment option. Online tickets to the Vatican Museums often sell out far in advance; without a ticket there is a very long line, and really no assurance you'll get in at all unless you show up early in the day.

Rome is blessed with many beautiful and varied churches. Except for St. Peter's, which has a security line that will look scary unless you prebook a timed entry online, and San Clemente (prebooking required), you can probably walk right into the other churches during their opening hours. Some take a significant break in the middle of the day, and some are not open at all after they close for lunch. There will be churches worth visiting near just about any sight you plan to see (though I'm not sure about Montemartini!).

Two favorite small churches of mine--both with lovely, very old mosaics--are located not too far from the Colosseum: Santa Prassede and Santa Pudenziana. At the time of my visit, Santa Prassede was open 10-12 AM and 4-6 PM (not sure whether that was seven days a week) and Santa Pudenziana was open Mon-Sat from 9 to 11:30 AM. Also in that area is the very large Santa Maria Maggiore. There are many, many others. It is very smart to have some 1-euro coins with you. Especially in churches that don't charge an entry fee, there may be a coin-fed box to turn on lights to illuminate mosaics, frescoes and/or sculptures. The Monti neighborhood located WSW of those three churches is a pleasant area for wandering around without crowds of tourists (at least there were not many there in March).

If you find yourselves in Trastevere, both Santa Maria in Trastevere and Santa Cecilia in Trastevere are lovely. Be sure to see the crypt at Santa Cecilia; it may close a bit earlier than the church itself.

Other than the Vatican Museums and the Villa Borghese, most of the museums (art and historical) and historic sites can be planned late; you just need to know what their days and hours of operation are. I walked right into the Capitoline and Montemartini in March 2023. The Villa Borghese will be busy but is capacity-controlled and more enjoyable than the Vatican Museums; it requires prebooking but is worth it. In the same part of town is the Quartiere Coppede, a lovely Art Nouveau neighborhood.

The Etruscan Museum at Villa Julia is very good, and GNAM (modern and contemporary art museum) is close by.

I don't have any walking limitations, so you should check distances on Google Maps to see whether places will be practical for you. Google's walking-time estimates are very useful in Rome, where you will sometimes encounter hills or detours necessary to avoid pay-to-enter areas like the Forum. Google's basic time allowance is 20 minutes per mile. If you see a walking route where more time than that is allowed, you can be pretty sure it's because you will encounter a hill or steps. I rarely use Google's walking routes because I like to explore, but in Rome Google's routes will help you avoid time-wasting and energy-costing mistakes like walking up and down a hill.

If you like art, there’s a bunch of churches in Rome with great art that you can just walk in. The first 6 listed below are right by the Pantheon, all relatively close to each other.

You can also walk into the Palazzo Barberini and the Galleria Doria Pamphilj for great art.

Churches:
Sant'Ignazio
Sant'Andrea della Valle
Chiesa del Gesù
Saint Mary of Minerva
Church of St. Louis of the French
Sant'Agnese in Agone

Santa Maria del Popolo
Santa Maria della Vittoria
Santa Maria Maggiore
San Giovanni in Laterano
Saint Cecilia in Trastevere
Santa Maria in Ara coeli
Santa Maria in Trastevere

Susan, you might enjoy a stroll through the ruin of Portico d'Ottavia in the Jewish Ghetto. It's free and has an interesting history. The remains of the Theatre of Marcellus are also nearby, and have been repurposed as a residential structure! Also nearby is the church of San Nicola in Carcere that has 3 Roman temples incorporated into its fabric.

https://www.turismoroma.it/en/places/portico-octavia
https://www.turismoroma.it/en/places/theatre-marcellus
https://www.turismoroma.it/en/places/basilica-di-san-nicola-carcere
https://www.churches-of-rome.info/CoR_Info/SNC045/San%20Nicola%20in%20Carcere.html

I'll agree that the Sistine/Vatican Museums is not an activity to be undertaken without prior reservation.

hey hey susan
so many things to see and do have been posted here. many churches listed which you can pick and choose. my own feelings, i'm not into seeing every church, i like to walk different neighborhoods. on the other side of "spectrum"
rome.us (under neighborhoods)
jewish ghetto quarters:
have some fried artichokes and other kosher food. years ago we did take a walk through here which has become an area to see nowdays.
quartiere coppede:
historical architecture and whimsical fountains, "house of fairies", fu fu & designers boutiques, gourmet food shops
shopping: farmers markets
gpsmycity.com
download app, self-guided audio walking tours. scroll around to see what they offer around rome and go at your own pace
another meaning for "art"
vineyarts.com
paint & wine party fun
crowntours.com/ rome
click menu, rome tours, scroll down to paint & sip: painting class with pizza & refreshments. fun day or evening away from crowds and lots of fun. souvenir to take home with you
oldfrascati.com
wine & lunch tour in the roman countryside, 35 minutes from rome in frascati. away from the hustle and bustle and crowds. take train to frascati, driver meets you there and then to winery, tour around the small village and then lunch.
read up "about us", family owned, walk thru the deli/oven that makes the "best porchetta sandwich" that i saw on a TV special few years ago. take some famous busom cookies home. this area is also home to the pope's summer villa and gardens.
secretroma.com
secret & free garden in piazza venezia (garden of palazzo)
few other suggestions for your spur of the moment, hope it helps and gives you ideas. enjoy & have a great time
aloha