Things To Do And See
I originally thought about producing some detailed descriptions of the various sights and locations of Venice but then thought: "Hey, it's all in the guidebooks". Rather, then, I offer a checklist of "must do" tourist things, tourist things it's not worth doing (in my view, anyway) and stuff that will enable you to say you've seen the other side of Venice. So, here goes: 
"Must Do" Tourist Things 

1, Basilica San Marco (Check out the Pala d'Oro altar screen and the Treasury for a few Euros) 
2, Piazza San Marco 
3. Take in the view from the top of the Campanile (It fell down in 1902 but the new one seems OK...) 
Doge's Palace and the Bridge of Sighs 
4. Rialto Bridge 
5, Peggy Guggenheim Museum (Palazzo Venier dei Leoni, Dorsoduro 701) 
Church of Santa Maria della Salute (The Plague Church) 
6. Church of San Giorgio Maggiore 
7. Church of Santa Maria Gloriosa dei Frari 
8. Accademia 
9. The Jewish Ghetto 
10, Arsenale Museum 
11. Take in the beauty of Ca' d'Oro from the Grand Canal 

Be My Guest, But.... 

Ride in a Gondola (Romantic but €80 for 40 minutes. I would recommend you choose a gondola ride that explores the back canals and avoids the Grand Canal)
Buy fake Murano glass. A lot of material comes in from China so check the provenance. Large dedicated stores are a better bet than tourist shops. Better still, buy in Murano itself. 

Off the Beaten Track:
Take the No 1 Vaporetto from San Marco (Valaressa) to Ca' d'Oro, sit back and enjoy the view. 
Watch the sparkle of the light on the Grand Canal 

Enjoy a peaceful walk alomg the canals of Canareggio (take in Tintoretto's house and the statues of the Moors - Fondamenta dei Mori) 

Visit the Rialto Food Market (Walk over the Rialto Bridge into San Polo, run the gauntlet of the tourist market and you'll find the fish and vegetable market situated to your right
Have a Bellini in Harry's Bar but be ready to say "Ouch!" when the bill arrives....
Find "The Most Beautiful Bookshop in the World". I'm not sure it's that beautiful but it sure is eccentric! (Hint: It's in Castello)
 Enjoy a Spritz with either Campari (bitter) or Aperol (sweeter)
Take tea in Caffe Florian. Byron used to visit but I doubt he paid these prices. (Piazza San Marco)
Put your foot onto the markers in the corner of Ponte dei Pugni "fighting bridge" (By Campo San Barabara, Dorsoduro). Enjoy researching why they're there. 

Buy some fruit from the floating barge moored at Campo San Barbara (right by the "fighting bridge"
Browse in Ca' Macana mask shop (near Campo San Barbara. Calle Cappelier/Calle Malvasia, Dorsoduro 3172. +39 041.2776142) 

Enjoy a gelato from "Il Doge" in Campo Santa Margherita
Take a glass of wine and some cicchetti in Cantina do Mori (see the route for the Market above. At the end of the tourist market turn left, then first right. The osteria is on the left). The full address is in the Eating and Drinking section
Visit the islands, particularly Burano and Torcello 

Take in the Klimts (along with other fines examples of modern art) at Ca'Pesaro, the Museum of Modern Art (Fondamenta Ca'Pesaro, Santa Croce 2076) 

Take a stroll along the Riva degli Schiavoni at sunset to take in Venice's special light and the views of San Giorgio Maggiore and Salute 
Finally, I would recommend looking through our Page on Venice Oddities for some real fun..