There is room for every mode of dress though I recall reading somewhere, perhaps here?, that one of the casinos won't permit sandals on men.

DH always wears shorts and a nicer shirt for dinner in the more upscale places, and a sundress or nice dress shorts/capris and top would take your wife anywhere. There are many places where beach shorts and a tee shirt might not be appropriate but there are plenty more casual places where it would be fine. It's basically no different than what you're used to doing in the VIs.