Waterbury is a big city. There are a lot of places where you could encounter street violence, but if you REALLY want to get punched in the face, I would specifically suggest these five locations:
Harris Circle/Long Hill/Berkeley Heights
If you read the Police blotter in the Republican-American regularly, you'll notice that Harris Circle shows up quite often. The names of the charged are typically followed by "Breach of Peace" or "Assault". Odds on getting punched in the face? 1:1
Oakville Ave/Whitewood Rd.
My dad owned the bar where Bobby D's now stands. It was a tough neighborhood back in the glorious 80s, and it still is. Don't mouth off or you'll see a fist flying in your direction.
Willow St./West Main St.
I spent many a night in Gahan's/Boru's over the years, and inevitably, a fist fight will break out in one of the parking lots around this intersection. The tolerance for stupidity is very low in this area.
East Main/Wolcott St/Wall Street
I've seen so many scraps at this intersection. My wife and I have fallen in love with Los Garcia's food truck on East Main Street, and we've passed by at least three fights taking place on our way there.
Town Plot Park
The go-to location to settle beef in Town Plot. For years, Kennedy, West Side, and Mount Carmel students take the short walk up Highland and Wilkenda Avenues to duke it out after school.
In conclusion, I'm not saying that these areas are specifically hazardous. It's just my observation as a Waterbury resident that these are the most likely places you risk being punched in the face in the Brass City.