I'm a native Floridian and have visited almost everywhere in Florida.
Google Maps
Is a Google map link to Fort Island Beach.. Near Crystal River.. Straight west of The Villages.
It has white-sand beach featuring covered picnic tables & restrooms, plus a boat ramp & a fishing pier.
The magazine cover beaches your thinking of are in the Panhandle of Florida, and much to far away for a day trip.
Google Maps
Example Google map link for Cape San Blas.
Clearwater south to Fort Myers also have great beaches but come with lots of Snow Birds traffic and over crowed beaches.