The Hyatt downtown is a A 5 minute drive from our place, we've stayed at the Hyatt many times and have enjoyed it. Unfortunately, The Four Seasons is under construction.
If you want to stay closer to the beach (20 minute drive), Hotel Palms is a great option. It's a really cute boutique hotel in Atlantic Beach.
If you're like to stay at a nearby Airbnb, we happen to have a hook up. You can contact Gili (Em's cousin, of course) who manages a handful of Airbnb's in San Marco. Check out the listings here. If you'd like to book one, you can contact Gili directly at +1 (850) 960-2582.