Welcome!
Start looking early for a place to rent, & secure it early. Mostly because rentals that allow pets are fewer. They exist, but are less common than the 'no pets' listings.
There are sites that advertise rentals:
Rent From A Villager | Rental Homes in The Villages Florida | Advertise Your Village Rental ,
this site we are currently on, under the Real Estate heading,
Couture Properties, LLC - Property Management & The Villages Rentals ,
403 Forbidden ,
https://*****************.com/ ,
VH4R Home Rentals in The Villages Florida The Villages Rentals ,
https://www.thevillageshpm.com/, & sites like **** & many others.
For beaches since we are centrally located you can either go west to the Gulf coast or east to the Atlantic beaches. Both are great options.