Dorado is located outside of San Juan (about 20 minutes without traffic, a lot longer with traffic). You will need a car to get there.
If this is your frist time, I strongly recomment that you stay in San Juan. Isla Verde, which is a 5 minutes drive from both the airport and Condado, and 15 minutes from Old San Juan, has the best beach in the San Juan area. Intercontinental and El San Juan are both on the beach and have nice pools. You won't need a rental car if you stay in San Juan.
For local food, try Bebo's near Condado, and La Bombonera and Cafe Manolin both in Old San Juan. All three offer delicious authentic food at good prices.