Most of the restaurants do have a dress code, particularly for dinner, though my experience is that they do not enforce it super strictly. Don’t show up to dinner in a bathing suit, cut-offs, or holey shorts and do wear a shirt with sleeves (avoid tanks) and you should be fine.
The one restaurant that does have a strict dress code is El Colonial, serving classic French gourmet cuisine. So, it is unlikely that you find me in there anyway. I know who I am… a taco and beer down on the beach at Beach Grill is more my style, but I digress. El Colonial will require men to wear long pants (I am not even bringing any, and I digress… yet again), a jacket, sleeved shirt or a polo.
I do recommend the Iberostar app to read about the dress code requirements at all of the dining establishments.