On a budget, weigh it — Rector's Palace isn't cheap for what it is.
~€18 (often on a combined museums pass)
The hook is one of history's oddest constitutions: the Rector of Ragusa governed for just one month, sealed inside this palace for the duration, forbidden to leave except on state business — a deliberate guard against any one man grabbing power, with the motto 'Obliti privatorum, publica curate' (forget private affairs, attend to public ones) carved over the council hall. Walk the period rooms and the serene arcaded courtyard and you feel how seriously this merchant republic engineered against tyranny. The honest catch is the museum collection itself is modest and a touch dusty for the ~€18 entry — it rewards the governance-curious more than casual sightseers, though the courtyard alone (a summer concert venue) is worth a peek.