La Fenice

You can google "dress code la fenice" for info on that question. As to the best venue, La Fenice is certainly the most important opera house in Venice. However, we enjoyed a shoestring production of La Boheme a couple of years ago at Scuola San Giovanni Evangelista for a fraction of the cost of La Fenice tickets. It goes without saying that the operas will be in Italian with no supratitles in English.

They probably won't deny you entry unless you dress unreasonably casual (like beach attire). However you might feel uncomfortable being too casual, since almost everybody will be dressed either formally or semi formally. Wear a pair of dark slacks or dark cotton pants (no jeans), a long sleeve dress shirt in any conservative solid color or light lined, i.e. not a Hawaiian shirt ( basically any shirt you'd wear in a business office environment, it doesn't have to have French cuffs), a tie would be better. If it's summer you can probably get away without a jacket, otherwise a jacket is a nice addition. It doesn't have to be a tuxedo, any nice business sport jacket that matches your pants will do. Basically wear business (smart) casual, and you'll look like a million dollars.

FWIW, my Italian instructor has told me that she never saw a man wearing a necktie but no jacket until she came to the States. Much more common is a jacket without a tie.

That's true. I never wear a tie without a jacket, but, if you don't have a jacket, you can always pretend you left if at your seat. Taking your jacket off is considered rude only in the most formal circumstances. But it would be ok at work in the office, or while dining in a less formal setting, for example. In that case you'd have a shirt with a tie while your jacket is on the chair.

Of course, if you really want to look Italian, check out this guy: Roman men Gotta love those shades. This photo was taken after Pentecost Mass at Santa Maria in Trastevere. The church was packed with locals.