The closest airport to Destin is VPS (Ft. Walton Beach) and is about 25 minutes from Destin. One hour away is a slightly larger airport PNS (Pensacola).
Numerous hotels are available near Emerald Coast Scuba. They range from the least expensive – Motel 6 850-837-0007 (call and ask for the weekly rate, not the nightly rate) or the Wingate Inn 850-654-4678. To rent a condo, try ResortQuest.com or VRBO.com.