There are regular flights from Quito to Esmeraldas, which pproximately takes 35 minutes and cost around 110 USD per person for a return ticket.
The transport from Esmeraldas to Atacames (40 km) is most suitable done by taxi and approximately costs 20 USD.
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By bus:
There are regular buses leaving from Quito to Atacames every day. This
journey, known for its beautiful scenery with a changing climate and
geography, has a duration of approximately 6 hours and costs 10 USD.