Monaco is expensive, so be very cautious with restaurants
Though a good dinner at Le Huit et Demi (Rue Langlé, La Condamine) will probably cost you at least 20 €, it's worth the price.
Planet Pasta (Rue Imberty, La Condamine) will serve you delicious pasta, and as it's one of the cheapest restaurants in town, you MUST book in advance, even on weekdays.
If you want to enjoy a good lunch in front of the sea and eat as much as you can, try the buffet at Gerhard Café (Fontvieille harbour).
The two main supermarkets are Carrefour and Casino (you can then joke about spending money at the Casino in Monaco). There's a market at Place d'Armes, but you'd rather cross the border and go to the market in Beausoleil.
Monaco wishing to keep its otherworldly reputation, street food isn't easy to find inside the borders. Go to the commercial mall around Carrefour or to the Beausoleil market.
Most local food is provençal food. The only real monegasque specialty is the Barbagiuan. It's a bit like an argentinian spinach empanada.