I'm fairly new to matplotlib and am limping along. That said, I haven't found an obvious answer to this question.
I have a scatter plot I wanted colored by groups, and it looked like plotting via a loop was the way to roll.
Here is my reproducible example, based on the first link above:
import matplotlib.pyplot as plt
import pandas as pd
from pydataset import data
df = data('mtcars').iloc[0:10]
df['car'] = df.index
fig, ax = plt.subplots(1)
plt.figure(figsize=(12, 9))
for ind in df.index:
    ax.scatter(df.loc[ind, 'wt'], df.loc[ind, 'mpg'], label=ind)
ax.legend(bbox_to_anchor=(1.05, 1), loc=2)
# plt.show()
# plt.savefig('file.png')
Uncommenting plt.show() yields what I want:

Searching around, it looked like plt.savefig() is the way to save a file; if I re-comment out plt.show() and run plt.savefig() instead, I get a blank white picture. This question, suggests this is cause by calling show() before savefig(), but I have it entirely commented out. Another question has a comment suggesting I can save the ax object directly, but that cuts off my legend:

The same question has an alternative that uses fig.savefig() instead. I get the same chopped legend.
There's this question which seems related, but I'm not plotting a DataFrame directly so I'm not sure how to apply the answer (where dtf is the pd.DataFrame they're plotting):
plot = dtf.plot()
fig = plot.get_figure()
fig.savefig("output.png")
Thanks for any suggestions.
Edit: to test the suggestion below to try tight_layout(), I ran this and still get a blank white image file:
fig, ax = plt.subplots(1)
plt.figure(figsize=(12, 9))
for ind in df.index:
    ax.scatter(df.loc[ind, 'wt'], df.loc[ind, 'mpg'], label=ind)
ax.legend(bbox_to_anchor=(1.05, 1), loc=2)
fig.tight_layout()
plt.savefig('test.png')
                Remove the line plt.figure(figsize=(12, 9)) and it will work as expected. I.e. call savefig before show.
The problem is that the figure being saved is the one created by plt.figure(), while all the data is plotted to ax which is created before that (and in a different figure, which is not the one being saved).
For saving the figure including the legend use the bbox_inches="tight" option
plt.savefig('test.png', bbox_inches="tight")
Of course saving the figure object directly is equally possible,
fig.savefig('test.png', bbox_inches="tight")
For a deeper understanding on how to move the legend out of the plot, see this answer.
Additional add-up on @ImportanceOfBeingErnest's answer, when bbox_inches='tight',  'pad_inches=0.1' may need to set to larger values. 
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