In
GuebaYol you'll certainly find them.
All I've seen here are imports. Mostly Asia. You find some in large department stores (Eg. Plaza Lama), in
Tiguere/Tiguera trapos (trashy clothing) outlets in Sosua and most other
tiguere riddled towns and most probably in the "stores" under the overpasses of Santo Domingo's "27" & Duarte as well as some stores on La Conde (SD's Colonial district) or Santiago's Calle Del Sol and side alleys... mostly dreadful quality.
There is also a souvenir shop inside Playa Dorada (POP) which had a large stock all sorts of hats.
As another poster suggested, once you find something acceptably close to what you were looking for, the lack of SIZES may further frustrate you search. Things come in here in single shipments... there is often no stock keeping and ordering.
I doubt the hat on the picture is REAL straw... maybe just some beige synthetic material, still, I haven't seen many looking that "good" in quality around here.
If you insist on REAL straw (
paja de toquilla / falsely labeled "Panama straw"), you may want to check out Ecuador... specifically the city of Cuenca (where MOST "Panama"-hats are made).
I don't know if they have picked up on the new "hip" designs... but that's where STRAW fedoras would be from.
... J-D.