It would probably be easiest in Google Earth, where you can directly save the extents to a JPEG. If you have a Pro Account, you can set the output resolution and also save to PDF.
Source.
You might also be interested in this which explains caching various places so that Google Earth can be used in offline mode. You can store up to 2GB of imagery this way, which is quite substantial.
Edit: Per your edit, it seems that GE is not for what you are looking. A manual way to solve your question would be to "print" the current view, which opens a new window. From there you can save the page as Web Page, complete
(in Firefox), which saves a folder containing the image. Inside said folder is an image aptly named staticmap.png.
You don't need to change the URL if you pan/zoom around, so you can save the page multiple times, thereby giving you your desired maps.
Assuming you save the files to a folder, this Python script will move all the images in the subfolders to the main folder specified at run time.
from Tkinter import Tk
from tkFileDialog import askdirectory
import os, shutil
Tk().withdraw()
folder = askdirectory()
for i,dirname in enumerate([x[0] for x in os.walk(folder) if x[0] != folder]):
old = "{0}\\staticmap.png".format(dirname)
name, ext = os.path.splitext(old)
new = "{0}{1}{2}".format(name, i, ext)
os.rename(old, new)
shutil.move(new, folder)