I've made a number of visits to the Bronx recently, from Katonah Avenue's Irish enclave to Riverdale's remaining Jewish delis, to Arthur Avenue and Pelham Bay, and to City Island as well.
Sammy's on City Island is loads of fun...and loads of food.
Liebman's is old-school deli that tastes just fine.
Arthur Avenue can be fine, if you know how to avoid the touristy food and schlock. Casa Della Mozzarella's fresh cheese is super, and the remaining butchers do a fine job.
Louie & Ernie's is great. Sit in their backyard and enjoy a sausage pie.
And for Cuban food, I like Havana Cafe, with 2 locations, though I've only been to E. Tremont.
Much more to explore in the coming months.