The Dragon Breeding Nest
Originally, you may only breed one Draggy, but after 10 6-hour periods, you unlock the ability to obtain a Furious Dragon. After another 10 6-hour periods, you get the chance to unlock the Lightning Draggy. After yet another 10 6-hour periods, you may get the Stormy Dragon. Then, you can get a Green Draggy after another 10 6-hour periods, and a Sayan Dragon after another 10 6-hour periods. After the Sayan Dragon, you'll need 100000 gold or 50 cash to start all over again.
Each period is free. It can be speed up to the next period with the use of 3 cash for a Draggy, and 15 cash for a Dragon.