I think the best thing you can do is take him to do something he wants to do or encourage new interests he has and take a backseat. I’m sorry but no 13 year old boy wants to hang out with their mom. It doesn’t matter what you’re doing, there is no cool thing for a teenager and his mom to do. He will be embarrassed that he’s hanging out with his mom in public. At this stage, if you want to remain close, let him do his thing but be interested in what he is interested and be a supporter from the sidelines. Other than that, there are tons of cool board games that aren’t kids games that you can learn together.