For romance, Getting Lost in the Back Calli delivers.
The single most-recommended 'free' thing in Venice: put the map away and follow the narrow calli, dead-end at canals, stumble on empty campi and artisan workshops the day-trippers never reach. Off the San Marco–Rialto–Ferrovia spine the city goes quiet and dreamlike fast. The catch: it can frustrate the goal-oriented, you will hit dead ends and bridges with stairs, and it pays off most in the morning/evening edges of the day.