I live in the mountains, but I have been stranded at the ocean during a Class 1 hurricane. It was exciting, to say the least!
I would hook my TT up to my vehicle, fuel up my tow vehicle, do whatever preparations must be done prior to the hurricane hitting your residence and then head out on some of the lesser used roadways - not Rt 17, I-95 or any of those. There will be hundreds of thousands of people trying to use them. Head inland about 200 miles, find a campground and setup for a fun weekend in the TT. It'll probably be raining off and on, maybe even all the time, but that far inland, it shouldn't be a problem. Even better, head toward Asheville, NC and plan to have a weekend in the mountains. Plan to get out by no later than Thursday afternoon.