As a couple, St Mark's Square (Piazza San Marco) works.
The colonnaded sweep, the basilica facade, the duelling cafe orchestras at Florian and Quadri — at dawn or after the day-trippers leave it is genuinely magical and free to simply stand in. The catch: by mid-morning it's a dense river of tour groups and selfie sticks, the cafes charge eye-watering sums plus a music surcharge, and in autumn/winter acqua alta can leave it under shin-deep water with raised duckboards.