Hidden beneath Palazzo Senatorio, and accessible via a tunnel linking Palazzo dei Conservatori to Palazzo Nuovo, the Tabularium was ancient Rome's central archive. The tunnel is lined with panels and inscriptions from ancient tombs, but more inspiring are the views over the Roman Forum from the brick-lined Tabularium itself.
Note that the Tabularium is part of the Capitoline Museums, so you'll need a ticket to access it.