I married into a (mostly) Italian-American family who live in Chicago. There's a deli on Harlem, close to Higgins, called Nottoli, and more than 50% of my visits to the in-laws involve going to said deli and grabbing an Italian sangwich. It's amazing.
Here in C-U, there are options for the same type of thing. Of course, there's Jimmy John's, and despite my misgivings about the corporation and the local operator of the locations, I still crush an Italian Night Club from time to time. I do a lot of things I shouldn't, so it's OK.
There's Cheese & Crackers as well, and they serve Mindy's Italian which is a good sangwich too. It's served on baguette, which is a little too rough for my taste, and I like my Italian sangwiches on Italian bread, but still, solid.
For me, however, the best of these sangwiches comes from the menu at Papa Del's, which is, of course, known for its Sicilian style pizza, a legendary meal around here.
It's hard to order anything but their pizza, but if you want to try something different off the menu, this sangwich is basically perfect. It's got everything you want, and the slices of meat are premium, and the bread is perfect for this sort of meal.
This is highly recommended. $10.00 USD. Comes with a side. I get mine with no tomato, because that's my preference. I frequently buy two, because wrapped up, and stored for a day, it almost tastes better. Not sure why.