As others have said, providing your house/apartment isn't actually on the beach (storm surge etc) the problem could be the rain that follows.
A category 1 hurricane isn't that big-a deal, tbh (considering they go up to 5!)
25 years ago I spend a boring Xmas with a boyfriend in a motel in Cairns, Australia, as Cyclone Joy, a Category 5, bore down on the town. It sat off shore for days, but the power was cut (trees down on power lines) and the water was cut (pumps at the dams failing due to electric shortage and debris in the turbines). We had a battery radio that was updating us- they put out a loud 'jingle' every time there's something new to report so you listen. We'd filled the bath tub and criss-crossed the motel windows with masking tape and worked out how to get the mattress into the bathroom (strongest part of a house). We knew where our evacuation station was an' all! Luckily, though the staff left, the owner didn't so all us guests, together, raided the fridges and made pot luck meals on the gas burners, then swam among the submerged pool furniture in the pool (you sling it in to stop it becoming a projectile). We knew how to entertain ourselves... but we weren't that worried as northern Queensland houses are built to withstand category 5 cyclones.
Eventually it drifted south, still at sea, and crossed the coast as a Category 1 halfway down Queensland.
The big problem was then the rain and getting out. There were no planes left as, having learned their lesson during cyclone Tracey (Darwin, 1974?5?) the airlines flew them all out; the flooding cut the N/S railway line and the Bruce Highway that circles Australia was washed out!
Took me 10 days to leave back to Brisbane in the end (on a train that went 200 miles inland to avoid the central coats flooding!), having cancelled my dive trip as the ocean was full of debris and silt.... and small cuts on my feet festered as the were constantly wet as the streets of Cairns were still awash.
I very much hope this is hype not reality for the poor Americans!