Right across from Plaza D'Italia at the corner of Commerce and Lafayette is M's Coffee and Cafe. They offer a wide array of po-boys and panini sandwiches for lunch, many right around $5. I had the pulled pork po-boy. Despite the bottled BBQ sauce, the meat was plentiful and well flavored. If you're in the Warehouse District around lunch time and are just looking for simple cafe fare at a good price, definitely consider stopping here.
Also, consider stopping at Plaza D'Italia before, after or to enjoy your lunch. For most of the year (excluding St. Joseph's day-March 19th) you will have the park to yourself.
2 days ago