Hi, Im from Ecuador. Each section has its own beauty. If you are looking for the warmest weather then the coast is it. The biggest city in Ecuador happens to be in the coast. It is Guayaquil and it has great beaches within at least 1 1/2 hour drive. (Great beaches in the coast are: Montañitas, punta carnero, libertad, salinas, playas). Another nice city in the coast is Manabi. If you want cooler weather the the highlands would be it. Quito, which is the capital of Ecuador is a must. It has the "middle of the world" monument that you can go up to. And it is actually IN the middle of the world as the ecuador line goes right through it. Otavalo is very very nice. it has a lot of arts and crafts done by the local indigenous people. Also Cuenca, Riobamba are beautiful cities to visit. If you are going to Ecuador, you HAVE TO visit the Galapagos Islands. A flight once in the country to the Islands (the only way to get there) is about $120-150 dollars if you are not from there. For locals is quite cheaper, like $60. They have the giant galapagos turtles, lots of fauna and flora. Animals and plants that you will not see anywhere else in the world. It is gorgeous and like Hawaii, there are little islands all around you can go to. The last section is the Amazon, I have never been there but I have read Puyo is pretty.
Make sure you take benadryl for insect bites if you go to the Amazon. Also the food may be a little to hard on your stomach if you are not used to rich meals. Taking tums or pepto will help.
Try to "fit in" with the locals. Robbers have an eye for foreigners. Wear clothes that are simple. Stay away from wearing any rings, watches, necklaces. Do not carry your passport with you. Cash and/or credit cards you might be taking put them in a "fake pocket". This is a square of cloth that you can saw inside of your pants. This is not meant to be scary but just need to be as careful as possible.
Hope this helps!