Hey MaryAnn! I actually just got back from Europe where I spent about 48 hours in Venice and it was so much fun! I had gotten a lot of recommendations before going there, but I'll break it down to all of my favorite things that you could do in 24 hours:
Here are the foods that you need to try in Venice: gelato, Italian pastries, espresso, and spritz. You can pretty much get those anywhere. The first three, I had in several random places that I stumbled upon and they were all awesome. The spritz is a cocktail and some places make them differently than others though, so I guess you'll have to try them everywhere ;)
Have fun! :)
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My biggest advice for Venice is to stay in Venice-proper overnight. Many people just come for the day and are disappointed by the crowds (and the heat and smell, in the summer). At night, Venice turns into a ghost town. It's really nice to stroll around the Piazza San Marco and down to the Riva Degli Schiavoni just before midnight and have it all to yourself.
If you only have a day, I would stick to Venice-proper. If you've never been before, I would stop by the Basilica di San Marco or the Doge's Palace (Palazzo Ducale) first thing in the morning. If you go to the Basilica, pay the few extra euros to go up to the balcony for a nice view of the square and the original bronze horses.
In the afternoon, as Debbie says, get lost! Make sure you see the Rialto Bridge and the outside of the Basilica di Santa Maria della Salute at some point, but otherwise, wandering toward the water in any direction will give you more of a feel for Venice than anything else.
Gondola rides are really overpriced, but I'm glad I did one when I visited in high school. A cheaper option (that I recommend) would be catching the #1 vaporetto down the length of the Grand Canal. It's not as romantic, but it's a nice way to see the whole thing by water, especially if you sit up front. If you want a cheap, quick trip in a gondola, traghettos can ferry you across the Grand Canal at a couple of points.
If you do want to go see one of the other islands, I'd skip Murano. While it's neat to see the glass being blown, the island is brown and dusty and most of the shops are just as expensive as Venice itself. Burano is more picturesque, with brightly colored houses and lace being sold instead of glass. I never got to San Michele and regret it.
I went to Harry's Bar to celebrate my 21st birthday with a bellini. It's one of those things that's overpriced and more fun to say you've done it than anything else, unless you have a major interest in Hemingway.
Gelato, pastries, and chocolate-covered espresso beans were my favorite Venetian treats. Stopping by little cafes for an espresso and a pastry was probably my favorite dining experience. The fruit from the produce boats and markets is a nice pick-me-up as well. There's one at Campo San Barnaba, which is perfect if you want to reinact the Venice scene from Indiana Jones and the Last Crusade as well.
Have an amazing time!
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La Mela Verde is the best ice cream place! My favourite flavour was white chocolate, almond and coconut. If you have a tight budget like we did, use the vaporetto (water taxi) - you can get day passes etc. We got the 48hr pass which allowed us to visit the two nearby islands of Murano Island and Burano which were well worth the visit!
I'm not much of an expert on Venice, but 2 years ago I went to visit some friends over there who happen to be Venice natives. They showed us around and brought us on somewhat of a pub crawl which was basically a spritz and a tiny tapa in about 9 or 10 different 'bars'. I unfortunately don't remember any names of places, but the little nugget of info that I did want to pass on is that alot of places have 3 separate menus - one for english speakers, one for italian speakers and one for those who speak venetian dialect, so the locals… and its not so much a price difference as it is different foods! so if you happen to befriend someone from venice maybe ask them about this.. i remember the food being amazing! Hope you have a great time :)
Also something i presonally loved was spending hours window shopping for venetian masks!
I've got a very special secret tip for you to discover a real Italian way to taste some great wine and good food. You should try out Bacareto da Lele (see here: Bacareto Da Lele on Yelp.com). It is a very small kind of wine and food place, where you get a glass of local wine for € 0.60 and really nice sandwiches for less then € 2.-. You get your food and drinks at the bar, where you also pay for them upon receipt, and then consume it outside, together with friends and family and other Venetians. This is a real Italian way of getting a tasty snack in between times. The owners are very helpful and friendly and are used to dealing with tourists not capable of the Italian language. You'll find it easily. See the walking route here. There's a big wine barrel used as a table in front of it. It's very close to the main station right across the German/Austrian consulate.
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Back from Venice, Rome and Amalfi. Thanks for the advice and input. We wandered the streets, got lost a tad, bar hopped (crawled as they call it) snacking and drinking. Sat in plazzas eating gelato and people watching. Lovely 24 hours! Browsed shops filled with leather goods, handpainted papers, lace and pastries. No real set itenerary as we were wearing off jet lag. I think that worked for the best!