
Congratulations, Eva,
I would recommend this:
Mass of the Solemnity of Mary, Mother of God, at St Peter's. The Holy Father will be celebrating it.
Leave the Basilica and wait before re-entering. (Have a coffee and a donut or something at a cafe -
not one on via della Conciliazione, the boulevard leading into the piazza- and relax.
Re-enter Basilica, see the Pieta (on right as you enter).
Proceed down the right side, notice the magnificent statue of Pius XII.
Stop at Blessed Sacrament Chapel; Adoration will probably be in progress. The Tabernacle is a replica of the Ark of the Covenant, complete with Seraphs.
Proceed down right side. Kiss foot of St Peter's bronze statue (lips to your hand to foot). Thank St Peter for all he did.
Move to crypt before Main altar. St Peter is buried below.
Move to the other side of baldochino (the thing above the main altar. When Bernini executed this marvel, he was told by his friends that it couldn't stand for any length of time).
On other side of b, look at the 4 columns and the statues on them. They have to do with the Passion.
Look straight above you and see the magnificent dome. (If you want to, you can take the elevator to see it, climb up to the very top of the Dome and see a great view of Rome.)
To the left of where you are standing, at a diagonal, there is the altar of Mary, Mother of the Church. Say a Prayer for Pope John Paul there and think of all of us here on OBOB.
Go to far end of the Basilica, see the Sedes Petri, the Chair of Peter (with statues of Ambrose and Athanasius "holding the chair up"). Above the statue the famous window of the Holy Spirit, not glass - it's amber or alabaster.
Walk back toward the entrance. The stairs and elevator to the roof are on your right near the rear. You will pass the Pauline Chapel (across from Sacrament chapel) which is usually locked.
Go back into Piazza. On the right and left of the monolith, you will find a round pavement stone. Stand on it and look at the colonade. You'll see an optical feat: only from that position can you see the columns as they are actually aligned; from everywhere else, you just see lots of columns.
Rest.
Take the double decker bus from station, capolinea (head of the line). This is on the other side of the colonade, to the right as you face the facade. It's just past the wall leading from the Vatican to the Castel S. Angelo (Hadrian's Tomb).
Ask the driver or someone to let you off near the top end of the via Nazionale. Take a cross street to S. Mary Major basilica. (Santa Maria Maggiore (mah-jor-ay))
Then take the bus to Ss. Giovani Laterano (Saints John Lateran). This is the Pope's Cathedral. Nearby you will find the Scala Santa, the Holy Stairway. It was brought by St Helena to Rome. It had been the stairs of the Roman Presidium which Our Lord climbed before he was sentenced by Pilate. These stairs are climbed on one's knees.
If you have any energy left, return to "il centro", the center of ancient Rome. There you can see the Piazza Venezia monument of Victor Emanuel ('big white wedding cake'), the Coloseo, Piazza di Spagna, Piazza Navona. The Forum will be closed on a holiday, but you can see much of it from the street.
Near the Forum and the wedding cake, there is a small church, under which is the prison where Peter spent some time. His chains are inanother Church, S Pietro in vincoli. This is a bit tricky to get to. You go up the via Cavour and look on your right for a staircase. At the top of it, you'll find the Church. The chains are in a glass container. There is also a magnificent statue of Moses by Michelangelo. It is so life-like, you'll half expect Moses to stand up at any minute.
The last of the four major basilicas is St Paul's outside the walls. You can get the bus to go there near the Coliseum. There is a plenary indulgence if you visit all four piously.
(St Peter's, Ss John lateran, St Mary Major, St Paul's 'fuore le mure', outside the walls).
Many great Churches in Rome. The Pantheon (Santa maria degli Martiri) is notable. The Gesu (Jesuit headquarters).
Too many to see. You would need a month.