Most people meet the Quirinale by accident, swept up to the Trevi Fountain in a crowd and never noticing the hill above it. Done deliberately, from the top down, it's a short walk through the best argument in Roman architecture — and the right way to reach the most famous fountain in the world.
Under three kilometres, best early. From Barberini, climb to Piazza del Quirinale, the highest of the seven hills, where the president's palace faces a long view to St Peter's. Then the duel: Bernini's Sant'Andrea, a jewel-box oval he loved above all his churches, and a hundred metres on Borromini's San Carlino, whose walls seem to breathe. They face off across the same street; stand between them.
Now come down the back lanes to the Trevi. Approach from above and the whole marble wall of it opens below you, instead of the slow shove up from the front. Go at first light or not at all.
Finish at the Galleria Sciarra, a painted Art Nouveau courtyard nobody walks into, then back to Barberini.