Weather wise there is not really a best time. The average temperature on Aruba is about 80 degrees Fahrenheit (27 degrees Celsius). The lowest temperature ever was 66 degrees Fahrenheit (19 degrees Celsius). You can expect more rain from October until December, but because Aruba lies outside the hurricane belt, so your chance of getting hit by one are slim to none.
We have a low season that goes from May until half December. Then it is more quiet on the island. The busiest times are during the Carnival Season (the whole month of February and the Holiday Season (half December).