There is a street parking scheme in the area of the house (Zona A) run by the council.
Parking is chargeable every day from 9 am to 1 pm and from 3 pm to 8 pm (accurate on 5/9/21, please double-check on street signs). You can pay at the local machines.
You can buy a weekly permit for €20 and park the car in any available place in front of the house or in any other place nearby.
Permits can be purchased in various shops of the city, but the closest to the house is "Edicola PP 29 Galli" which is a newspaper kiosk in the pine wood. It is open everyday from 8.30 am to 7.30pm. It is 950m away within 10 minutes walking (you can go directly by car as well). By the way ... it is on your way to the beach!
For more information, you can look at the official website of the parking company (in Italian)
Edicola PP 29 Galli
Viale Michelangelo Buonarroti, 64
55049 Viareggio (LU)