Hi Robin,
Are you referring to the Galapagos Islands? If so, it is possible to travel to the islands on your own. It's quite simple. You book a flight from the coast town of Guayaquil to the Galapagos Islands. It is about $400 for a return ticket. 0nce you are in Puerto Ayora on the Galapagos Islands you start shopping for a boat (I paid $50 a day). You will pay half the price of the agencies in Quito. You will need time to do this.
Ecuador is a very beautiful country and is an excellent destination for a first trip to South America.
Hightlights of Ecuador
Whatever you decide to do, join one of Travel Amazing South America's tours or explore Ecuador by yourself, you will have the time of your life.
Enjoy your trip! Keep us posted!