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I will be working in Sicily, Italy for about a month. Specifically, in Messina. I very much enjoy my keto diet. I assume I will be socializing and going to restaurants with my coworkers.

Will it be possible, both practically and culturally, to eat mostly meat and vegetables while there?

Like for example, when they bring me to a restaurant for dinner, will most restaurants have a "hunk of meat" dish? If I eat only veggies, will everyone look at me like I'm crazy?

I don't know about Sicily specifically but in most of Italy this would not be much of a problem. Italians are big on fruits, vegetables, meat & fish. Of course they are even bigger on pasta and pizza :-).

A typical Italian restaurant menu has multiple sections: antipasti (appetizers), primi (lots of pastas), secondi (generally meats, fish), contorni or insalata (vegetables and salads), formaggi (cheese course), and dolci (desserts).

Almost all restaurants have full sized salads and many appetizers that are carb free or low in carbs. Primi are carb monsters: pasta, gnocchi, etc but Secondi tend to be mostly meat or fish and veggies.

It may cost you though: Secondi tend to be the most expensive things on the menu. A "hunk of meat" does not come cheap in Italy: they often value quality over quantity.

It is quite typical in Italy to have meat and carbohydrates as separate courses. For example, one of the primi piatti (often pasta) and then one of the secondi piatti (often meat or fish without many sides).

It is very normal to have one or the other rather than both, maybe with an antipasto or a dessert. (http://www.taste-of-italy.com/2014/12/antipasto-primo-secondo-how-to-order.html)

Only ordering from the secondi piatti will likely get the sort of diet you are looking for