My favorite church in Rome...

...is the The Basilica of St. Mary of the Angels and the Martyrs (Santa Maria degli Angeli e dei Martiri).

This church was designed by Michelangelo in 1561. It incorporates the ruins of the Baths of Diocletian (which were built on that spot in 306 AD). The entrance of the church seems very modest until you realize that it is the original wall of an ancient Roman ruin. Instead of covering it up, Michelangelo wanted us to see it, which seems like a really modern architectural choice to me (exposed brick?) During the Renaissance people didn't know what these ruins were or how they were made, but were in awe of their size and the skill it took to build them.

In 1702 a meridian line/sundial was built inside the basilica. Pope Clement XI had it built because he wanted to check the accuracy of the Gregorian reformation of the calendar and to produce a tool to predict Easter exactly. 

From Wikipedia:
The sundial was built here because (1) Like other baths in Rome, the building was already naturally southerly oriented, so as to receive unobstructed exposure to the sun; (2) the height of the walls allowed for a long line to measure the sun's progress through the year more precisely; (3) the ancient walls had long since stopped settling into the ground, ensuring that carefully calibrated observational instruments set in them would not move out of place; and (4) because it was set in the former baths of Diocletian, it would symbolically represent a victory of the Christian calendar over the earlier pagan calendar.

Amazing!

Here is a picture of the beautiful oculus at the top of the dome. There are little planets and stars in the stained glass. It really is a thing of wonder: