1) I was at the zoo to look at the animals.
This tells why you were at the zoo.
2) I was at the zoo looking at the animals.
This tells what you were doing at the zoo, but doesn't say much about the primary reason you were at the zoo. (Maybe you went there to see a particular animal, or to meet your niece and nephew.)
3) I went to the zoo to look at the animals.
This pretty much means the same as the first sentence, although the first might be a better one to use if you were going to report something else, as in:
I was at the zoo looking at the animals when a lion suddenly escaped!
All of these are valid constructs, and some might sound a little better than others in certain contexts. For example, has someone just asked you why you went to the zoo? Or are you setting the context for a long story?