I am jealous.  I was last in that area in 2010 and I miss it.  But anyhow, these are some of the places that you'll have to try to fit into your schedule:

Food:

• Ostaria Boccadoro -- great seafood spot that's a bit off the beaten path
• Locanda cipriani -- this place is a Venice institution. Ernest Hemingway and royalty have eaten here
• Antiche Carampane -- one of the cities oldest restaurants. Tons of celebrities have eaten here

Gelato:

• Boutique Del Gelato -- always a long line but worth the wait
• Alaska Gelateria -- some of the most creative gelato flavors I've ever seen, like fennel and artichoke

Bars:

• Naranzaria -- fantastic view of the canal
• Bancogiro -- also a great view of the canal
• Ardidos -- super cool decor
• Al Merca' -- semi outdoors; enjoy drinks in a huge shaded patio
• Skyline Rooftop Bar -- awesome view Venice from above
• Pane Vino e San Daniele -- wine bar
• Ristorante Maddalena -- their house wine comes from their own vineyards

Attractions

• Campanile di San Marco -- another spot for an awesome view of Venice
• Basilica di San Marco, Doge's Palace (Palazzo Ducale), Torre dell'Orologio

Of course, you have to for a gondola ride on the canal. Have a  blast!

If glass blowing interests you at all, you should ferry over to  Murano Island.  So pretty!  You can watch glass being blown and pick up some souvenirs.

And you HAVE to go to Boutique Del Gelato.  I waited in line for it once a day.  That's how good it is!  I tried a bunch of different flavors and my favorite was nicciolosa, which was pretty much vanilla gelato mixed with Nutella.  But you can't go wrong with anything you order there.  Also, a gigantic scoop is only 1.5 euro!

48 hours is a tight time frame, but if you're ambitious and energetic enough, I think you can definitely get a good feel for the city since it's so tiny.

Here are some of the most popular cultural attractions:

• Gallerie dell'Accademia: tons of art inside of an old church
  
• Cà d'Oro: an awesome castle right on the canal that's full of art and cool furniture
  
• Grand Canal: Speaking of canal, of course you have to sail on a gondola or some other boat through it
  
• Piazza San Marco: you can see the famous bronze horses and Campanile here, plus so much more.  While here, you should grab a bite at one of these outdoor cafes:  Caffè Florian,  Gran Caffè Quadri and  Gran Caffe Chioggia
  
• Doge's Palace (Palazzo Ducale): another castle full of art
  
• Punta della Dogana: yet another palazzo with art, but this one of the contemporary nature
  
• Peggy Guggenheim Collection: don't know how into art you are, but some of the world's most famous pieces are here.  I didn't go though, because it costs between $200-$600 to get in, depending on peak seasons, but if you love art, it might be worth it.
  
• There are tons of churches in Venice (and all of Italy actually), but here are the most famous: Basilica di Santa Maria Gloriosa dei Frari,  Chiesa Di San Giovanni e Paolo, Chiesa Della Pietà, and  Scuola Grande Di San Rocco

For food:

• Rosa Salva is very close to the Chiesa Dei Santi Giovanni e Paolo.  Super old cafe that's been there for centuries.
  
• Al Covo: So good. Apparently manned by American-Italians.
  
• Da Fiore: amazing seafood.  Prix fixe meal is about $100 or so.
  
• Osteria alle Testiere: another seafood place.  Really creative dishes, like octopus-stuffed gnocchi
  
• If you like wine,  Cantina Do Mori and  Cantine del Vino Già Schiavi are great wine bars with awesome charcuterie plates.

My stomach just growled writing that.  Have a good time!

Hello Debbie,

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.

Enjoy!

Stephan

Whoever's going to visit Venice must stop at the  il Paradiso Perduto  (in  Cannaregio) for lunch, dinner or just an happy hour! Happy hour with locals runs also at  Campo Santa Margherita, don't miss it! Any "bacaro" would be good after six p.m.!

If you wanna try some tipical food you gotta go to  Antica Trattoria Poste Vecie (close to the  Rialto Bridge). 

Wanna have some party? If you're lucky try to go at  PalazzinaG Hotel (in  Sestiere di San Marco).

In summer, if you want to get a nice tan, go to  Zattere and enjoy the panorama. :)

I was literally at Caffè del Doge every morning that I was in Venice.  They have such a great selection of coffee, imported from all over the world, and very good croissants.  All their staff speak fairly good English, too, so it was easier to chat it up with them.

For gelato, Alaska Gelateria is the best!  Be prepared to wait in line.  Such amazing flavors. 

For a hotel, The Gritti Palace is one of my favorite hotels in the entire world, so check it out. It just recently went under a $55 million renovation.