Castello d'Empuries is easiest by car, about 15 minutes from Figueres and a little over an hour from Girona. Buses connect it with Figueres and Roses, but frequencies are not ideal for a rushed day trip.
The nearest useful rail station is Figueres. From there, take a bus or taxi, or combine Castello with Empuriabrava and the Aiguamolls by car.