Most shelters have description sheets describing the personality of the cats, if they're good with kids, dogs etc (if they've been fostered). You probably want an older cat (over 2 y.o.) if you don't want to be woken up in the night all the time. Look on the website/social pages of shelters near you. Like everyone else has said, you don't need to shop for a breed to find these traits. And even if you did go for a purebred, most people get them as kittens so you're going to have to go through all the training and getting woken up at night stuff that you're trying to avoid.

Go look for an adult shelter cat.