If you want to discover South America but have only a few weeks in front of you, Ecuador is certainly the destination I will recommend. Andes, coast, amazon rainforest, traditions, colonial history… you can experience in Ecuador most of what South America has to offer, without wasting too much time in transportation (the country is one of the smallest of the continent).
In this article I put together my recommended itineraries for 2 or 3 weeks, both will allow you to discover the country and many of the things it has to offer. You will also get ideas for alternatives and practical information about transportation.