Still a difficult way to visit a city like Rome, a two-days foray into the city atleast gives you the chance to not having to choose between St. Peter's Basilica and the Vatican Museums OR the Colosseum - you can do both!
Day One: Colosseum/Roman Forum/Palatine Hill
Refer to our "Itinerary: Rome in One Day" post to know the specifics of where to go and where to access the archaeological site once faced with the Colosseum.
Since you have more time, though, take the time to really explore the area around the Colosseum thoroughly. Choices for your walk to the Colosseum can include departing from the subway stop at San Giovanni (see post mentioned above) or from the one at Circo Massimo (same!).
You could take it a step further and take a long route at San Giovanni: instead of walking towards via di San Giovanni in Laterano, take a via dell'Amba Aradam, on your left while you wait to cross the square. Can't miss it! In ten minutes time you'll have a via della Navicella on your right, climbing up to the Caelian Hill - turn there and admire some of the most beautiful churches of Rome - Santo Stefano Rotondo, with a remarkable round structure is on your right while the Chiesa of Santa Maria in Domnica alla Navicella (familarly referred as - simply - "La Navicella") is almost opposite that, on your left.
Plus, you could enjoy the park at Villa Celimontana, also on your right - one of Rome's smallest, loveliest green public areas.
Also on your right, after la Navicella, is a via di San Paolo della Croce - at the end of it, enjoy the Santi Giovanni e Paolo Basilica - on the side of the church it's possible to visit the Roman houses discovered underneath.
Or you could continue walking to the Colosseum - keep going in a straight line until via della Navicella opens in a huge square and changes its name into "via Claudia": you should see the unmistakable shape of the amphitheater from where you are!
Once done with your tour of the Colosseum/Roman Forum/Palatine Hill, you can choose among different possibilities before you head back to your accommodation:
1. You could climb the stairs on the side of the exit at the Colosseo subway station, walk on a via degli Annibaldi in a straight line until you reach via Cavour: keep going ahead and you'll be in the cosy, picturesque and lively Monti district - a slightly saner version of Trastevere!
2. Walk uphill on via di San Giovanni in Laterano until you reach the Basilica di San Clemente and visit that one!
3. Walk along via dei Fori Imperiali, reaching the Trajan's Markets Museum (the entrance is on via IV Novembre, uphill from piazza Venezia);
4. Visit the Vittoriano on piazza Venezia, along with the Museo Nazionale di Palazzo Venezia (with your back to the monument, it's the building on your left in the square);
5. Proceed to the Wax Museum or the underground Roman houses at Palazzo Valentini (also on via IV Novembre, opposite the Wax Museum: needs booking);
6. Visit the Capitoline Hill and its museums;
7. Continue your walk to the Jewish Ghetto and the Trastevere district.
As always, we recommend doing what you're comfortable with, not what you "feel" you have to do because you're in Rome!
Day Two: St. Peter's Basilica/Vatican Museums/ Castel Sant'Angelo
For specifics about this itinerary, also refer to the second half of our "Itinerary: Rome in One Day" post. The route is exactly the same, except you can definitely relax more along the way. For instance, if you want to enjoy some shopping while walking towards Castel Sant'Angelo, don't walk down via Stefano Porcari from piazza del Risorgimento: instead, with your back to the Vatican walls, look for a via Cola di Rienzo, on the right - that's one of the main shopping boulevards in central Rome. To head to Castel Sant'Angelo when you're done with that part of the day, simply reach a crossing with a via Cicerone on your right - walk down it until you reach piazza Cavour, with a huge cinema ("Adriano") and a majestic white building (part of the Hall of Justice). Castel Sant'Angelo is precisely on the side of said building.
When you're done with all your visiting, you could very well keep on visiting the city center, as you have much more time on your hands. Choices include:
1. Crossing Ponte degli Angeli to reach corso Vittorio Emanuele (on your right at the end of the bridge). From there, either walk down the street or take a bus to reach Campo de' Fiori, Piazza Navona, Largo di Torre Argentina (in this order) and from this last stop, the Pantheon. To explore the area around Piazza Navona do read our dedicated post!
2. Feeling like climbing a hill? Get a bus to the Janiculum Hill from outside the entrance of the Santo Spirito Hospital and follow our "Green Trastevere" itinerary backwards!
3. From Largo di Torre Argentina, explore the area and then reach the Jewish Ghetto, on your right along via delle Botteghe Oscure and then taking a right on any alley you prefer.
4. From the Pantheon, go backwards and explore the church of Santa Maria Sopra Minerva, which means precisely that the building stands above a temple to the Roman goddess. Also, from here you can reach in no time the lovely piazza di Pietra, the Parliament Square or Fontana di Trevi (again, take whatever alley on your left if facing the Pantheon).
5. Again from Largo di Torre Argentina, you can follow the tramway tracks towards the river: the Trastevere district begins at the end of the bridge.
(The picture at the top of this post comes courtesy of Wikipedia user Danbu14 through a Creative Commons License)