For a Malagan jamón, you should go to one of the traditional restaurants in Malaga old town. In my opinion, El Pimpi, one of the oldest Bodega serves the best jamón in town. El Pimpi is an inexpensive restaurant in the center of the city (Calle Alcazabilla) where you can try many typical Spanish dishes and tapas. It is frequented by tourists and locals alike. If you are getting down from the cruise hungry, go to La Sureña, an excellent restaurant in the port area (Muelle Uno).
If you want to try the typical Málaga Campero (I recommend you do), you should go to Maruchi. This place is located in El Palo, so you will have to go east of the city (take the 11 or 3 bus). You can spend some time on the beaches in El Palo while you’re there. Maruchi serves the best camperos and is a favorite among young locals.
The locals also frequent many of the chiringuitos that you can find pretty much anywhere near the beaches in Pedregalejo or El Palo, where you can try typical seafood dishes and the famous “espetos”, as well as paella or gazpacho.
You must also visit Malaga indoor market, Mercado De Atarazana to try fish tapas. Make sure you try as many tapas as you can. Just bear in mind that you have to eat standing up.
For less traditional food, you can try a restaurant called Noviembre, in the center of the city, near teatro Cervantes, or Picnic, a nice hipster-y restaurant in Soho.
For vegetarians, Cañadú in Plaza de la Merced is one of the best places with vegan and vegetarian options. Also, Burger La Calle in Pedregalejo has great burgers.