We’ve stayed in Puerto Plata and Cabarete. Shorts/sandals are acceptable in most discos and casual bars and most cafes, etc., but for dining out in the evening, it is generally expected that long pants/skirts/dresses and shirts with sleeves (no tank tops, muscle shirts) as dinner is typically a much more formal mealtime, it’s a cultural issue that we always respect. However, not every bar/restaurant/cafe has a strict dresscode.
It’s best to check before you actually go to these places just to make sure and save yourself the embarassment of being underdressed or overly dressed. After all, you want to be comfortable, but also respectful.
Most bars are casual, but please no bathing suits unless it specifically caters to that sort of informal attire! I was horrified to see tourists in thongs and Speedos in a beachside bar in Cabarete around supper time. There’s a time and place to be completely casual, but please, when I’m trying to enjoy a meal, put some clothes on and have some respect!