My girls are 13 and 11. They are both too old to call getting together with their friends "play dates" My 11 year old started getting embarrassed by that term a few years ago. I think it was when the "Diary of a Wimpy Kid" movies or books referenced the word "play date"
For a balance of social time vs other ways to spend their time, I tend to follow my kids' leads, within reason of course.
My oldest is a true extrovert. She has always spent most summer days growing up with neighbor friends, and maybe a few friends she has kept in touch with from school. This year its 100% a small group of school friends that keep in touch, text constantly, and hang out. I'm out of the loop on planning, except to be asked permission and kept informed of their whereabouts. Like most parents, I have a strict "no friends in the house when I'm not home" rule, so they need to find ways to get together at a park or coffee shop or whatever when parents are at work. It was great that she planned and rode her bike to the pool with some friends today. Last Friday evening she had some friends over to the house, some boys, DH and I made sure we stayed here the whole time to supervise. If she asked to do the same Sat night, we would have said no because WE wanted to go out for dinner and a movie. But it turns out she went over to a girlfriend's house the next evening anyway. I let her go out with friends any time it's possible, unless we have a prior commitment. Honestly, she's had really tough 7th and 8th grade years, and I'm just happy to support whatever brings her comfort and joy, which is at age 13, is her friends. And they are good kids. She and her friends don't have much if any money, so it's mostly just spending time together.
My youngest is an introvert, and she has a small handful of friends. She's just fine hanging out at home with her sister or her family. But she is always willing when a friend calls and invites her to do something. She gets invited out and over a lot. She's so busy accepting invites, she doesn't have much time to do the inviting herself. And honestly, she is kind of lazy about making that effort. I encourage her to be a good friend and reciprocate sleepovers, etc, but I don't force it, or push any kind of formal take turns system like we had done when the girls were in preschool. Sometimes I feel guilty about that, but at this age, it's really her own relationships to build or to neglect, not mine to micromanage. There is one friend of hers that calls ALL THE TIME and wants to spend 24/7 with her. I had to tell her to please just leave one message when I saw her number on caller ID 37 times! She's a nice girl, and has a very nice family, but this friend definitely is the one seeking my DD out all the time. I find myself wishing she would mix it up a bit with a few other friends, but that is her world to figure out. But since she calls my DD continually, we often have to say no to them making plans because we have family obligations, it's too late in the evening or she is out with another friend. Sometimes she' ask again a few hours later, so yeah, I think she has a hard time taking no for answer, but I should try to be more understanding because he probably doesn't see other options, and it is nice she likes my DD so much.