None of these restaurants are touristy. Google them, see which one suits you for price and location.
Very pricey but worth it:
Cracco (One of the most famous chefs in Milan. This would be the splurge)
Still pricey but less so, great food:
Innocente Evasioni
Alice Ristorante
Unico
Asola
Moderately priced, great food:
L’ Essenziale
Antica Trattoria Morivione
L'Altra Isola
Sambuco dell’Hotel Hermitage
Budget, neighborhood type restaurants but still great:
L'Osteria del Treno (very close to Milano Centrale train station)
Ponte Rosa (located on the Naviglio Canal, a good neighborhood to hang out)
Al Pont de Ferr (also on the canal)
Marta
Belli Freschi
Aromando
Il Liberty
Ratana'
Trattoria del Nuovo Macello
Osteria dell' Aquabella
Pasta Madre
Masuelli San Marco
The most traditional dishes are probably cotoletto, ossobucco, and risotto, if you want to really eat alla Milanese.