If you’d like to enjoy some of the 25 museums in Genoa, the most convenient option is to buy a card for 1-2 days or the full year. More info on this website.
Cash & Cards
Despite credit cards are broadly used as well as debit cards, in Italy you may still find places where they are not accepted or “out of order”. You should therefore have always a bit of cash with you and use it for all expenses below 20 EUR.