Built as a cylindrical mausoleum by Rome's Emperor Hadrian on the Tiber river just east of what is now the Vatican, the Castel Sant Angelo was converted into a military fortress before the Pope fortified it in the 14th century. The edifice is is named after the statue of Archangel Michele (Michael) found on the very top. Castel Sant'Angelo is now a museum, the Museo Nazionale de Castel Sant'Angelo.
You'll be able to take guided visits or visits via audioguides. There is access for mobility impaired people, and a bookshop.
On the top floor there is a cafe with great views of Rome. If you get there early for lunch, it may be possible to snag a table with a great view of St. Peters. The prices are not outrageous, and the coffee is good.
Find current prices and information in Italian: Museo Castel Sant' Angelo.
Bus lines 80, 87, 280 and 492 will get you close to the Castle. You'll find a taxi stand at Piazza P. Paoli. From the center near the Piazza Farnese, it is a very nice walk down the Via Giulia and then, after a right turn at the Tiber, a walk over the Sant Angelo Bridge, which is lined with statues, as you see in the picture on the upper right.
A visit to Castel Sant Angelo can easily be combined with a trip to the Vatican.
Castel Sant Angelo Renovations
Recently, it has been discovered the the Castel Sant'Angelo was in a poor state of repair. Italy will pump 1 million Euros into fixing the castle, after carrying out immediate repairs costing 100,000 Euros. This activity may impact your visit.
More on Castel Sant Angelo
The Castle has five floors. The first has a winding ramp of Roman Construction, the second features the prison cells, the third is the military floor with big courtyards, the fourth is the floor of the popes, and contains the most magnificent art, and the fifth is a huge terrace with a fine view of the city.
In 1277, Castel Sant'Angelo was connected to the Vatican by a rather infamous corridor called the Passetto di Borgo , allowing the castle to become a refuge of Popes when Rome was under seige. Castel Sant'Angelo was an equal opportunity castle, it also hosted popes in its prisons. You can clearly see the Passetto running on the north side of the aptly named Via dei Corridori, the "way of the corridors", on a Google Map. The Passetto can be visited only occasionally, as explained on the Atlas Obscura page
Puccini's opera Tosca was set in Rome, and features the ringing of the bells of Castel Sant'Angelo. Puccini made a trip to Rome "or the sole purpose of determining the pitch, timbre and pattern of the bells. He even climbed to the top of the tower at the Castel Sant'Angelo to clearly experience the Matin bells, rung in the morning by all the area churches and heard in Act Three of Tosca." The third act of Tosca is set at Sant Angelo.