In downtown Rome is the Palazzo Barberini, today’s National Gallery of Antique Art, with magnificent paintings such as Raphael’s La Fornarina (his mistress) and Holbein’s Henry VIII. However, unbeknownst to most visitors is the magnificent rear “secret garden” (formal garden with ubiquitous fountain) which is even hidden below from the Piazza Barberini (with Bernini’s great Triton Fountain) it overlooks. And hidden within the Palazzo Barberini’s hidden garden is a Mithraeum - a buried 1st-century AD Roman temple, dedicated to the Persian God Mithras, complete with dazzling frescoes. (It’s even unknown to most Romans, unlike the more famous Mithraeum at the lowest level of St. Clemente near the Colosseum.)
In Rome just don’t visit the Vatican Museums. Venture behind the museum’s interlocking buildings to visit the extensive Vatican Gardens with its many pavilions and gardens.
Here’s a tip: When inside any palace, museum or church, just look out the windows so you can see what you may be missing.
There’s only one time I don’t recommend walking around to see all-four sides of a building -- when the building is round.