I wanted to save it to the computer so I could access on the move if I needed to rather than printing. I don't have a mobile internet access. Am I right in thinking if I saved to "My Maps" I'd need internet access?
It really depends on whether you want interactive or not.
If I just want a picture of the basic map I 'copy' it then put a new page into photoshop and paste it there. I can then chop and change it to suit my needs and finally save it as a PSD, a PDF or a JPEG.
Depending on the size picture that you want - you could do a 'screen grab' and cut and paste from there.
I think that if you want an interactive 'My Maps' type google map then you need the internet on to use it.