There aren't many laundromats in a country where you can pay someone to wash your clothes for peanuts.
Either do that, or there's a decent drop-off laundry service/dry cleaners in Punta Cana Village - Bubbles Cleaners, Tel. 809 959 0357. There are one or two in Ver?n, one near Plaza Genaro and one further up the road (direction of Higuey) called something like El Bosque. You can also rent washing machines by the hour.