Sorry, Elise, I just reread your post where you did ask for restaurant suggestions for lunch…
1) Roma luncheonette, right across from the Italian American Roman Catholic church, Mount Carmel…open for lunch only, but with some of the best parmigiana sandwiches you could ask for.
2) Down on 187th Street, the Full Moon Pizzeria…a real neighborhood joint, but honestly, some of the best pizza you will eat in New York. Note: whole pies tend to taste better than the slices. Regardless, it’s all very tasty!
3) On Arthur Avenue, Mario’s is a little fancier, but still very reasonable..good pasta, seafood dishes
4) Across from Mario’s is Emilia’s, another very nice "red sauce" Italian place…good pasta, chicken, veal, etc.
5) The consensus of most New York "foodies" and Italian food fans is that the gold standard in that part of Little Italy is Roberto’s, on Crescent Avenue. Superb food, some very inventive dishes, very nice setting, but long waits are common.
6) Right up the street from Roberto’s is Il Fiume, which I like a lot. Nice atmosphere, good service, good, solid food.
All of these places (with the possible exception of Roberto’s, depending on what you get) are extremely reasonable price-wise. That’s the other advantage of being out of Manhattan; the prices are generally lower.
Walk back to 187th Street to get your pastries and coffee at deLillo’s, or at any one of a number of other good places.
I hope you enjoy, wherever you go!