This is pretty old already, but I bet more people will hit it, so I'll put the answer here. It seems to be a surprisingly common issue that doesn't have an answer anywhere.
Note how the error complains about api.client but not evernote.
Traceback (most recent call last):
File "<string>", line 1, in <module>
ImportError: No module named api.client
Most likely, the problem is that OP has a script in his path called evernote.py, which I guess is a common name people use to name their first evernote script. Rename the script to something less obvious and that should do the trick.