The only place in St. John I'd recommend with your restrictions is Caneel Bay, and even then, I'm not sure it will work with your budget. St. John is lovely but very hilly, and I think it would be challenging for visitors with mobility issues.
There are also the Hanalei Plantation Cottages on the North Shore of Kauai. One was used in the filming of The Descendants. They're pricey, and they book up:
http://www.hanaleiland.com/hanalei_rentals/beach_cottages.html