As one commenter pointed out, the simplest solution is to use the USERPROFILE environment variable to write the file path. This would look something like:
import os
userprofile = os.environ['USERPROFILE']
path = os.path.join(userprofile, 'Documents', 'ArcGIS', 'file1.gdb')
Or even more simply (with better platform-independence, as this will work on Mac OSX/Linux, too; credit to Abhijit's answer below):
import os
path = os.path.join(os.path.expanduser('~'), 'Documents', 'ArcGIS', 'file1.gdb')
Both of the above may have some portability issues across Windows versions, since Microsoft has been known to change the name of the "Documents" folder back and forth from "My Documents".
If you want a Windows-portable way to get the "Documents" folder, see the code here: https://stackoverflow.com/questions/3858851#3859336