I was going to suggest looking in the San Terezno, Lerici area on the south side of the Bay of La Spezia. Lerici is more resorty with a harbor and castle over looking the coast and beaches start just south of Lerici. Sam Terezno was a fishing village and is smaller and mellower in tenor with many beaches - free and Italian lido style. It would be a train to La Spezia and then a bus or taxi to either of these towns. They are connected by a coast waterfront walkway with beaches along the way.
In the surrounding area - Porto Venere is across the bay - reachable by ferry - and tiny Tellaro is reachable by bus. Inland Sarzana is over the hill by bus from Lerici.
Any area with a beach will be filled with people taking to the beach by the end of June. Excluding the towns of the CT you are more likely to encounter Italian heading to the beach for the summer than American daytrippers.
I'd love to carve out a week or two to explore this coastal area more, but if I was going back for the beach part this is where I would return to.
Have a great trip,
=Tod