Since I last posted, I located an Italian-language page for Villa Viani, which seems to be about 50-75 mi from Genoa. It has pictures, including a picture at the top that I assume is an aerial view of the town.
http://www.villavianiproloco.it/portal/alias__villavianiproloco/lang__it/tabID__5802/DesktopDefault.aspx
The home page that you can click on shows a map, which enlarged has the villa and nearby roads going down to the sea at Imperia. Given that assistance I was able to find the villa on one of the European road atlas webpages.
Thank you to Angela as well for confirming that there really is such a villa, which had been family lore for so long.
Bob