Because of its unique geography, Venice has a remarkable number of paths for its size, and it is a wonderful place in which to get lost. The city is entirely founded on artificial islands formed by ancient wooden piles with limestone on top of them as foundations for the buildings. As a result, with little possibility of expansion, the buildings take up as much space as possible, leaving just narrow paths and the canals as the main means of transport.
There is a wonderful randomness about Venice’s footways; not only are they narrow but also their direction can hardly be predicted. Bridges over the channels do not always go the way you want, and the main routes will wander seemingly at random. Many routes are little more than alleys and often go under buildings; the sotoportego, a right of way through an arch under a building, is a common sight.
A few canals were filled in during the 19th century, forming wider ways, but the main paths are narrow and frankly can barely cope with the number of tourists. So to explore Venice, it is best to try to get away from the main routes. It is worth making sure that you have a good navigation program on your phone, but inevitably, you will get lost at least once, that is part of the charm, and whatever route you take, there will be buildings worth seeing and discoveries to be made.
Just as with footpaths in the country, it helps to understand why the paths were developed. Foot navigation tends to go from campo to campo, the various squares at the center of each parish, each with its own church; if you follow the main routes, you will find yourself moving from church to church. And there are lots of those in Venice.
So as not to wander aimlessly, it helps to have a reason for your wanderings, and here, there are plenty. Venice is a waterborne city, so if you want to explore the grand mansions which line the Grand Canal and other main waterways, then getting into a boat is necessary. Gondola rides cost around 80 euros per hour, and of course, you may have to put up with the gondolier singing Neapolitan popular songs (the traditional Venetian ones seem to have disappeared). The main water-bus (vaporetto) routes take you down the arteries, so catching route number one is also a good way of exploring the Grand Canal.
But at some point, you need to start wandering by foot. JG Links’ wonderful Venice for Pleasure is a great choice for first-time visitors to Venice. It includes a series of delightful walks all around the center of the city with very detailed instructions, thus, enabling you to explore all the major buildings while having someone navigate for you. There are even suggestions for stops and, Venice being what it is, restaurants like the Locanda Montin (Dorsoduro 1147, Venezia, Italy on the Fondamenta Borgo) are still there and still highly recommended.
One problem with random wandering is that many of the churches, key places for art lovers in Venice, can be closed for lunch. There is now a group of churches, CHORUS, which offer a 12 euro pass for entry into all 17 churches, and most have opening hours that run all day. The churches encompass some of the major sights in Venice, such as the wonderful Stations of the Cross by Giandomenico Tiepolo (son of the more famous Giambattista Tiepolo) at the church of San Polo, the Veronese painting and frescoes that cover every surface of San Sebastiano or the sequence of tombs and altarpieces which fill the Basilica of Santa Maria Gloriosa dei Frari, while the church of Santa Maria dei Miracoli is a wonder in itself. Most have significant paintings, and one of the delights of wandering around is to encounter an altarpiece by Titian still in its original location such as Titian’s San Giovanni Elemosinario at the church of the same name, the merchant’s church close by the Rialto market.
There are other trails that you can take. There are a number of surviving Scuole Grande, religious confraternities which accumulated a remarkable quantity of great art, some of which are still in place. The Scuola Grande del Carmini has a wonderful cycle of paintings by Tiepolo, while the Scuola Grande di San Rocco has a stupendous number of decorations by Tintoretto.
If you find the accumulation of Old Masters a little too much, then seek out the work of the Modernist architect Carlo Scarpa who was a Venetian and worked on a number of projects in his hometown. The Galleries of the Accademia has work by him, as does the Palazzo Querini Stampalia (which is open to the public Tuesday to Sunday 10am to 6pm).