Vieques is a pretty safe island, but use common sense when visiting the more remote beaches. Leave your valuables such as passports, credit cards, and any other important documents and electronics at your place of lodging. Take enough cash for you to buy drinks and lunch on a beach day.
If you have rented a vehicle to get around to the various beaches this is a must actually it is highly recommended to not leave any valuables in the vehicle and to leave the doors unlocked; the idea behind this is that if your doors are locked then there must be something of value inside and it is worth breaking the windows to check and see.
Familia Rios Laundromat
The business hours are apparently not set in stone, however it's rumored that should you call, you might be able to convince someone to open the door during what's supposed to be regular business hours.