The main reason to come to Cox’s Bazar is for the beach. It’s a very long, very exposed stretch of sand, rather than a picturesque tropical-island type of affair. It's fun for a quick paddle, though, and there are sun loungers and umbrellas you can rent (from Tk 10). The main attraction, though, is being able to take lazy sunset walks along the sand. There is also a handful of decent beach cafes.
If you want more secluded spots for either sunbathing or swimming, try heading about 10km south to Himachari Beach (Tk 200 in a CNG from Kolatoli Circle) or, better still, a further 15km to Inani Beach (Tk 300).