Also, the CY Oceanfront is miles nicer than CY Mayo Clinic... that place is horrible.
So in short, I recommend 5 miles north to CY Oceanfront Jax Beach or 5 miles south to Marriott Sawgrass in Ponte Vedra.
If it were me and I were Federal government I'd run away from the Mayo Clinic... the Mayo properties are the worst properties in all of Jacksonville anyway. That front desk clerk may have been doing you a favor.