I think once they hit the teen years, you don't need to think so much about "do" as just "be." Most of our kids' lives is scripted around identifiable events, right? When they're little, you Go To The Park -- as much to get yourself out of the house as to get the kid some exercise. And then there are lessons and clubs and after-school activities and all that. But then by the time they are teenagers, they don't need all that scheduling and likely have lost interest in a lot of the lessons and things, and they are capable of functioning independently -- so if you are desperate to get out of the house, you don't need to invent a "fun event" to do with your kid. But without those scripted, scheduled Things To Do, it does feel different, and it can be easy to sort of drift into your own separate circles.
So, first, recognize that some of this is normal. Kids that age do tend to pull away from their parents, because they are figuring out who they are independent of you. So less time doing things together is totally normal. The key is to adjust your own expectations: you no longer need to plan and schedule capital-A-"activities" to spend good time with your kid. At that age, they can and should be learning life skills, like cooking dinner and cleaning the house and balancing a checkbook and being physically active and reading and finding hobbies and all that. So ask your kid to cook dinner one night, and putter around the kitchen doing dishes or paying bills while s/he is doing that,* so you can be together without any pressure. Or do what my DH does and kick your kid off the TV to go shoot some hoops, or turn some pens on the lathe, or go lift weights, or whatever other thing my DH feels like doing -- if you want to go for a walk in the woods, tell your kid to come along. Or do what I do and force your kid to watch classic (i.e., bad) '80s movies with you -- this weekend, DH was gone, so I made us all watch The Lost Boys to get in the Halloween spirit, and then DD asked me to help on her college essays. The thing is, it's all low-key and unscripted -- we're just living life.
Parenting at this age is a shift. Treat them less like toddlers who need to be entertained every minute and more like adults who you like hanging around with.
*This sounds like a super boring childhood, right? But some of my best memories were puttering in the kitchen with my Granny, feeling like a grown-up helping with the canning and freezing and such. When DH is traveling, I send DS to get Saturday morning bagels instead, and you can see him puff up with the responsibility.