Good for you! Ecuador has amazing places to visit. Since Ecuador is a very small country you can pretty much visit a lot of places in two weeks.
I would start in the northern part of Ecuador: You can visit Ibarra and there are three big lakes in the same province that you can visit, Yahuarcocha, Cuicocha, and San Pablo. You can rent a bike and go biking around the San Pablo Lake; you'll be done in about 2 hours. In Cuicocha, you can have a nice trip in a canoe for about 30 minutes and then, in Yahuarcocha, hopefully, you'll be lucky enough to have the chance of assisting to one of the car races there. There’s a nice race track around the lake and usually international competitions take place during the weekend (summer).
If you like hiking, you can visit some of the many mountains, like El Cayambe, Cotopaxi, Chimborazo, Tungurahua, etc. Make sure to do some research on the one you would like to go because these are also active volcanoes and you may not be able to visit them on the mean time.
If you are planning to go to the Eastern part of the country (Oriente) where the jungle is at, you can visit Jumanji which is a kind of tour that will take you through the safe zones in the jungle (probably 1-2 days).
If you like to go to the beach, Ecuador has many choices. Beaches you want to visit are: Esmeraldas, Manta, and Salinas.
In Quito, the capital, you can find a lot of colonial arquitectural art in El Centro Historico. There are a lot of museums all over the city. Ah! and in Guayaquil, the place to visit is El Malecon 2000.
Have fun and a nice trip! =)