A good way to see churches, especially San Marco which has long queues every day, is to check out the mass times and turn up for mass. San Giorgio dei Greci have a very long mass on a sunday morning during which people come and go so you could pop in to hear the singing and admire the beautiful church. You can view mass times at various churches here.
There are little surprises in many buildings. For instance there is a gorgeous Rubens drawing in Santa Maria del Giglio and a wonderful Titian in the Gesuiti. You will discover your own in the many guidebooks in the flat and online.
You can find a good list of classical concerts on the Classic Tic website.
Many churches have concerts now and again - look out for posters.
The ‘Musica a Palazzo’ is delightful although the voices vary in quality. Likewise the Fenice where there is no resident company but sometimes they have very good visiting productions. The theatre (rebuilt after a fire) is spectacular. View their website here.
Museums & Exhibitions
You can book most big things online including tours of San Marco, the Doge’s Palace and the Orologio and the museums. Click here to visit a good site to view and book these major attractions. Some of the churches are run by Chorus and charge entry but not so many that it’s worth buying a season ticket IMO.
Big contemporary art exhibitions are often staged over two sites: the Palazzo Grassi (near Accademia) and the Dogana.
The Fortuny Museum is a charming building near Santo Stefano but only open when there is a temporary exhibition.
All of the below have their own websites or can be researched online for more information. Most are community occasions, no ticket needed, to turn up and watch and buy food, and maybe wear a costume if you feel like it.
The Biennale | Website | Book your tickets online and maybe take two days to see the whole thing. One day at the pavilions in Giardini and the other in the Arsenale venue. You might want to save yourself some time and energy by reading all the reviews (Guardian, FT Weekend) before you go so you know what you really want to see. You will come across lots of other events linked to the Biennale that you can pop into if you wish.
Carnevale | Website | World famous for its elaborate masks takes place in February, ending on Shrove Tuesday.
Festa del Redentore | Celebrated on the third Sunday of July with fireworks the night before. A festival with a big boat showing centred on the Redentore church, Giudecca. While you’re there take a look at the Tre Oci gallery (website here).
Festa della Sensa | Ascension Day (the date of which vaires, but is typically in May). Huge festival with all the local boat clubs out in force and the traditional marriage of Venice and the Sea, the doge now being represented by the Mayor.
Voga Longa | Website | An opportunity for boating competitions amongst local clubs etc, held in late May or June.
Regata Storica | Website | Similar to voga longa but in 16th century costume. Typically held in early September.
Venice Film Festival | Website | 11 days in late summer when the Lido is infiltrated by Hollywood stars. The centre of the experience is the Excelsior and the Cinema opposite.
Art Night Venezia | Website | A collection of cultural events run through Ca’Foscari University of Venice, usually in early October.
Venice Jazz Festival | Website | 5 week festival of jazz concerts. They have run both summer and autumn editions so check their site if you’re interested.