It is not uncommon to hear people casually refer to a place populated by tourists as a "tourist place." I think "tourist destination" is a little more widely used than "tourist place," but that is just my opinion. "Touristic place" is technically the grammatically correct one, since "touristic" is an adjective and "tourist" is a noun. But in daily conversation, I'm more likely to hear "tourist place" than "touristic place." This can happen with other words too. For example, I've heard people call clothes that tourists wear "tourist clothes" and never "touristic clothes." Good observation!