In the face of a travel downturn, Governor Charlie Crist exhorted industry figures to promote Florida, despite a $10 million cut to the state’s tourism budget. In July, hotel occupancy in Broward County fell 6 percent and average daily rates dropped 13 percent. Revenue for available rooms, the industry benchmark, dove 18 percent to $78 a day. Palm Beach County hotels fared even worse, with revenue per available room sliding 26 percent to $85 a day, Smith Travel said. In July, the average hotel room in Miami-Dade — South Florida’s largest hotel market — went for $117 a night, 9 percent less than a year ago. Jorge Pesquera, president of the Palm Beach County Convention and Convention Bureau, said heavy promotions were slowing visitor declines.