Reddit mentions of Streetwise Rome Map - Laminated City Center Street Map of Rome, Italy - Folding pocket size travel map with metro map, subway

First I would recommend getting this map. It's laminated and not too large, but on the back it actually lists every single street which makes it absolutely impossible to get lost. Rome is extremely walkable - can I ask what area you are staying in? The metro is convenient for getting to some areas and same with the buses, especially after a long day of walking, but I'd recommend getting to an area and then traveling by foot all day.

So I am sure you know the usual. The Vatican museum is extremely large and you could spend all day in there if you wanted to, but since you are not a huge museum person you can skip it or do it in one day with St. Peter's. St. Peter's Basilica - definitely spend some time wandering around here as well. It's intimidating in size yet has a cozy feeling to it. Down the street is Castel Sant'Angelo which is where the Popes would go if the Vatican was threatened. Up top are some great views of St. Peter's and of all of Rome - look for the wall connecting to the Vatican, that is where the hallway is that still connects the two.

Piazza Navona should be seen during the day, but I also recommend coming early morning so you can own the square. If you like wine, there's a restaurant near by, Cul De Sac, that had the most options in Rome last time I was there. Across the street is Campo de Fiori which is a flower/fruit market/tourist trap that is fun to wander around irregardless. You can get to the Jewish Ghetto easily from here, but I'll bump back to that later. The Pantheon is an incredibly easy walk from Piazza Navona and two of my favorite churches are right here. The first is Santa Maria Sopra Minerva which is behind the Pantheon to the left (there's a statue of Jesus by Michelangelo by the front alter) and Gesu which is out on the main street. While you are there, go scope out Torre Argentina which are ruins below street level - it is believed that this is where Caesar was killed. In the Jewish Ghetto I recommend starting at the Portico of Octavia - there are ruins here but also some harsh history of what happened to the Roman Jews during WWII. Do you like desert? There's is a bakery nearby that has no name that makes pizza ebraica (Jewish pizza) that is so delicious. It's cash only and is the corner door where via del portico d'ottavia and piazza costaguti intersect.

Do the Trevi Fountain in the morning to get to actually see it but head back at night to watch the bustle around it - don't accept anyone's offer to take your picture for you, but have fun watching other tourists get scammed. Climb the Spanish Steps but head left at the top for a nice walk with a view out over the city - you can head down into Piazza del Popolo and walk down Via del Corso which is one of the main streets in the city with a ton of shopping on it. You can rent bikes at Borghese park (to your back before you take the steps down into Popolo) and ride around - the lake is small but beautiful and there are some fun things to discover. I know you do not like museums, but consider the Borghese Gallery. It requires a reservation and is very small, but contains two statues by Bernini that will amaze you that someone can do that with marble.

The ticket for the Colosseum is a group one that also includes the Roman Forum and Palatine Hill (which are connected but each have their own entrance). I recommend starting at Circo Massimo for a view of the Palatine Hill, buying the ticket at the Palatine Hill entrance (weave up to your left) and exploring that before heading down into the Roman Forum (plus you will get some great views up top of both the Roman Forum and Colosseum). Head to the left to pass the line at the Colosseum entrance. The Altar of the Fatherland (giant white obnoxious thing with the winged chariots up top) offers another great view and has the tomb of the unknown soldier housed there. Capitoline Hill has a great museum and stairs designed by Michelangelo (who knew he was a stair designer as well?) - the museum has views of the Roman Forum that are great.

Otherwise, there are four Papal Basilicas (three others than St. Peter's) if you are interested. My favorite restaurant is off of the Piramide metro stop and is just a three minute walk down the street to La Valle del Sacco (I lived near here though, so I am biased). Check out the Protestant Cemetery by the pyramid (by the way, there's a decent sized pyramid here) to see Keats grave, if you are interested (very melodramatic after a rain). The Trajan Forum is a fun ruin location that is not crowded with tourists and has some great history. You can see the Baths of Carcalla (near the Colosseum), San Pietro in Vincoli (church that has the chains that held St. Peter and contains parts of an unfinished tomb by Michelangelo).

You can take a day trip by bus to Tivoli to see Villa d'Este with a gorgeous house and gardens and a crap ton of fountains - the town itself is also fun to wander around. I know you have Orvieto on there as a place you are spending the night, but you could also easily do it as a day trip from Rome - it's an hour by train and something like just 14 euros round trip. It's a very small town. Gorgeous, but extremely small. You could spend a full day there if you meander slowly and stop for a nice long dinner. The sunset is spectacular there though because it turns the stone into an almost clay red. I'd recommend staying in Siena for the day trips you mentioned - it's a bigger city and has more to do and just do a day trip from Rome to Orvieto.