Re: which island?
Wow you really plan ahead! I'm sure your pretty psyched about the trip :)
I've never fished in Nantucket but I know the Vineyard has great surf casting. Late September is a great time, the run should be on, and it coincides with their big tournament (note lots of fun, cool people, more crowded fishing than usual). I have off roaded on the Vineyard beaches but to be honest that was when I was young and we didn't care about regulations all that much so I'm not sure what the rules are for that. You can probably google it though. Good luck!