Some of the best things we've eaten in Palermo have been devoured far from a restaurant table, on our feet: the city's street-food vendors rival its fine-dining establishments in innovation and excellence. Don't believe us? Head to Ballarò Market, one of the oldest of its kind in the city, where the island's Arabic, Italian, Mediterranean and West African influences collide. Take a stroll through the organised chaos to feast on pane e panelle (sandwiches stuffed with chickpea fritters), deep-fried octopus, pani ca' meusa (spleen and ricotta buns) and thick slices of sfincione (fluffy Sicilian pizza), followed by ricotta-stuffed cannoli and prickly pears.

Inspired by Parisian café culture, this cocoa-obsessed destination is a bohemian haven on a hot Sicilian afternoon. Housed inside the city's historic public baths, near Piazza Marina, the interior is all twinkling fairy lights, second-hand books and upcycled furniture, with paintings and illustrations by local artists on the walls. Outside, in the leafy courtyard, potted palm trees and crumbling stone statues make for a characterful corner where locals and expats like to while away a few hours with a good book. Chocolate desserts feature heavily on the menu, but the multi-layered carrot cake is worth a try, too. In winter, rich hot chocolate is poured from vintage teapots at your table.

"What Balls" is the literal translation of this street-food kiosk's name, and a fitting one, as it only sells one thing: arancini. With flavours ranging from prawn and pistachio (weirdly good) to slow-cooked ragù (a classic) and, for those with a sweet tooth, Nutella, it's easy to make a full meal out of these iconic Sicilian snacks. Order a local Messina beer, subtly flavoured with sea salt, for the full experience.

This award-winning ice-cream shop has a small queue outside when it opens at 10am (11am on Sundays) - a clear sign that the gelato here is some of the best in Palermo. Flavours are strictly natural - no bubble-gum blue or sickly sweet pink in sight - and owner Antonio Cappadonia is meticulous in ensuring all ingredients have a pedigree provenance. Peaches are sourced from Montagnola del Monti Sicani; pomegranates from Caltavutoro; the almonds are Puglia's best; and pistachios are the vivid-green kind that grow so well in Bronte, on the slopes of Etna. If you're overwhelmed by the sheer number of flavours on offer, order a scoop of Antonio's favourite, the ingenious orange and fennel, which is inspired by a classic Sicilian winter salad.

Trattoria Gagini takes its name from Renaissance sculptor Antonello Gagini, whose 16th-century workshop once sat within the restaurant's thick stone walls. The spirit of Sicily's historic grandeur feels decidedly present here: guests share long, candlelit banqueting tables for a tasting menu inspired by the island's slow food movement. Sicilian-Brazilian chef Mauricio Zillo's menu won him a Michelin star last year - a credit to his playful take on classics. The wine cellar is well curated, with a focus on small Sicilian producers and a growing selection of natural wines.

With a proud history dating back to 1834, Antica Focacceria San Francesco continues to pull in workmen and large local families come lunchtime, who bypass the bewildered tourists trying to work out the ordering system. Go for the tabulè alla Siciliana (a traditional couscous mixed with seasonal vegetables) or anelletti al forno (little rings of pasta baked with ragù into a sort of tart). Otherwise, keep it simple with an ancient grain-based focaccia filled with caciocavallo sheep's cheese, anchovies and herbs, best enjoyed on a bench in Piazza San Francesco, one of the loveliest squares in the city.

Eating out in Palermo can be a touch meat-heavy, but it wasn't always this way: the city has a culinary history of creative vegetarian dishes, born out of necessity in the kitchens of the poor. New kid on the block aTipico plays with this veg-focused heritage, serving the likes of caponata (a thick-cut aubergine and tomato sauce) and pistacchiosa (a traditional savoury pistachio cream) with smoked and roasted tofu, and squid-ink risotto with a contemporary twist.

The Bisso family's first restaurant had to shut down after mafia intimidation, but Dario Bisso remains staunchly against pizzo (bribes). His new restaurant is located in Libreria Dante, an old, 1870s bookshop with many of the original period details and decor still intact. The terrace on the pedestrianised road overlooks I Quattro Canti, a magnificent baroque crossroads that marks the historic and cultural heart of Palermo. Flavours from across Sicily are worked into the menu: our order is an appetiser of polpette di melanzane - aubergine meatballs - followed by an umami-packed primo of homemade pasta with fried zucchini and mint, and a plate of a Sicilian staple involtini di pesce spada - swordfish rolls covered in tomato and breadcrumbs.