This little museum is just around the corner from the Cathedral di San Lorenzo. Admission is 6 euros per person, but, as we learned when we were leaving, this admission also includes a visit to the Museo di Tesoro, a museum of treasures in the cathedral. Note that both these museums are closed for an extended time midday. When we were there, they were closed between noon and 4pm.
This museum contains many pieces of art important to Genoa and its history from several centuries. We especially enjoyed the "Blu di Genova" and exhibit of blue fabric decorated with religious art. This fabric was the precursor of blue jean material (the info suggested that the word "jeans" came from Genoa). These pieces were impressive and distinctive.
Museo del Tesoro was smaller but interesting. Contains impressive silver work and relic purportedly related to John the Baptist.