Old Gold ... seeing Spanish is the language of Ecuador, and knowing what Banos translates as, the "funky" Banos hot springs do sound VERY interesting!
Guayaquil is coastal but beware is a VERY dangerous DUMP to be honest. Quito is superb. Very like many cities in Peru .. located high, in the crater of a volcano. The Metropolitan Touring "autoferro" (tourist bus on train tracks!) trip is a "must". Goes down the Andes from Quito to the coast through the "Avenue Of The Volcanoes" and the Devil's Nose, one of, if not THE steepest train descents in the world. All on rails and sleepers that have not had maintenance for 50 years it looks like!
My personal tip would be to add a week and go to the Galapagos Islands .. one of the great tourist spots on earth for nature and wonder. Flights go from either Quito or Guayaquil.
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~ Glen ~