Every exchange offers its wallet. But you should know, that exchanges are quite a touchy subject for certain people and with good reason; a lot of users have arrived too recently to remember the many, many, many exchanges that have fallen victim to hacks, seizures, shut-downs and outright exit scams. There has been millions of dollars stolen by, from and through exchanges over the years and so be careful when you're asking about the most trusted exchanges, because often the biggest exchanges are the ones which fall hardest.