1. For the ultimate Venetian Coffee Experience: Cafe Florian
This is the coffee house in Venice - and frankly, the first coffee house in Europe so how can you not go? It's expensive, no getting around that, but look, it's been there nearly 300 years and will be there probably 300 more, barring Venice sinking into oblivion, so you're paying for a lot more than just coffee.
To make the most out of the experience, prepare yourself for sticker shock in advance to avoid discussing it while you're there (incidentally, a cappucino is about ten euros), go earlier in the morning before the lines form, and to get a good table next to regulars, don't dress like a tourist. This means leather shoes/boots instead of sneakers, a coat instead of windbreaker, tailored pants, nice purse, quality scarf and of course, legit shades (even if it's cloudy and/or rainy). Order the coffee or drink of choice, and enjoy the view or conversation, as opposed to taking 23 pictures of you sitting there with a coffee. It's an experience that's best left just to romantic memory.
2. Best Coffee for Breakfast on the Run: Bar AmericanoThis place is located right off of the square beneath the clock tower, but functions almost as a local coffee bar . This isn't the place to whittle away the hours - the service is strictly stand up only. Make sure to order and pay at the cashier, cappucino and cornetto or an espresso and veneziana (a sort of fried doughnut pastry) are the way to go. Enjoy it at the bar over lively people watching - you'll notice the city get more crowded by the minute as the day trippers find their way to the square and enjoy the Mad Men era wood paneling and lighting fixtures that are as classic as they come.
3. Best Coffee on the Canal: Bar Tiepolo at the Westin Europa and Regina
Why this place isn't completely packed is beyond me - in fact, just the opposite is true. Many times (and this is a place where we've whittled away many an hour) we have the entire terrace to ourselves. Located on the Grand Canal on a floating terrace behind the Westin hotel, the bar serves creamy cappucinos served with plates of little cookies (including the famous Venetian "S" cookies) that practically constitutes an entire breakfast or afternoon snack. Soak up the rays and enjoy the Venetian traffic jams of vaporetti, service boats, gondolas, and motoscafi plowing towards each other at full speed - occassionally, you hear the singing gondoliers and accordion players as well. Afterwards, walk the marble hallway like Matt Damon did in the Talented Mr. Ripley.