I think that sports actually can be a great outlet, yes it attracts social/popular girls, but girls who are great athletes and work hard are valued no matter what their personality, and for high school, being on a varsity or JV team gives a girl visibility and a sense of purpose. Both my DDs were very athletic, one was also very social and she would have been included in social events no matter what, but the other was someone who found it hard to reach out to other kids and make friends, felt more comfortable with boys, hated "drama" particularly in MS and 9th grade. Sports teams in school and out really gave her a purpose and an outlet, and it helped that her entire outside of school team was actually weirdly full of introverts and somewhat socially awkward kids just like her, maybe in part because of this they all chose to practice a lot and had lots of success, and all of them made their varsity teams as freshman and contributed and got playing time immediately.
So for this summer make sure you find out about preseason and tryouts if she does a fall sport (and if she doesn't what about trying one not requiring prior experience, at some schools always looking for field hockey players, cross-country runners) and find out if there are informal summer "playarounds" or conditioning sessions she can show up at.
And what about some local sports camps and clinics?
Outdoors programs/camps like Caleva might also be a good place for her, and then there is always overnight camp.
Once a bit older programs like NOLS can be great, or some of the biking trips for teens, but those can be pricey, not sure whether that is an issue or not.