Love Gioia's, but my go-to's for sandwiches on The Hill are: Eovaldi's and Adrianna's. Charlie's Market is also a good spot to try.
Mom's Deli is closed, for now, but planning to re-open on Hampton near Eichelberger.
My recs for Italian restaurants on The Hill, in no particular order: Gian Tony's, Favazza's, Lorenzo's and Charlie Gitto's. Dominic's is also very good.