Growing up in NYC, I loved getting an Italian Ice on a hot summer day from one of the sidewalk vendors; it was a small cool and tasty treat in the heat that wasn't as heavy as ice cream but was as much fun to eat.
The only Italian Ice shop I have ever seen here in Los Angeles is Di Dio's in Santa Monica. For those people familiar with Hawaiian shaved ice, this is similar, but smaller and more intense; the flavors are not simply drizzled onto ice, but they are infused with it, making the flavors more intense; also because choices are not just from syrups but from real fruit juices, Italian ices can come in a range of flavors like Blood Orange, Coconut, Mango, and Strawberry.
At Di Dio's, you can mix two flavors in a single small serving (more if you get a larger container), so go ahead and experiment with whatever strikes your palate as a good combo. For people who prefer creamy confections, they also serve gelato, so you can have your ice and gelato too!