When you encounter this bird it is passive unless you take its egg. It's battle attacks are a spin attack and it does the most damage. The other one is a bite attack at it's not as effective. So when in battle do a spin attack to beat your foes.
The grassy area between the north zone 2 and the north zone 3, is full of pteranodons, sense it is a wide area, it is a great spawning place for large quantities of Dino's, just be careful, there have been many sightings of raptors roaming around- good luck.
If your having trouble finding high level pteranodons, I'd suggest going to the redwoods and bring some spike walls just in case so you and the bird can't get attacked by terror birds or any other threats there.. for any level/easy tame, look around the 2 tropical islands, usually the only threats there are compys and dilos