I have stayed various times at the Sheraton. Basic high rise but very central location on a main street and in a main square. Had view of the government buildings in front and mountains from my room.
The Hotel Delfin is nice with its playful dolphins you can view from the lobby bar. Another nice property is Apartohotel Las Americas. Not familiar with Doubletree but have heard nice things.
Be sure to factor in time to go to and from the airport. There seems to be no highway or direct connection between the two and taxis ran $17USD one way!!
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"Fly me to the moon and let me earn alot of miles."